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Hilbert Journal of Mathematical Analysis
Published by Komunitas Analisis Matematika Indonesia
ISSN : -     EISSN : 29857619     DOI : https://doi.org/10.62918
Core Subject : Science, Education, Engineering,
Chemistry Control & Systems Engineering Engineering Mathematics Physics
Hilbert Journal of Mathematical Analysis (Hilbert J. Math. Anal.) is a peer-reviewed, open-access international journal publishing original and high-quality research papers that treat mathematical analysis, geometry, topology, and all closely related topics. It is published by Komunitas Analisis Matematika Indonesia (Kamindo)/Indonesian Mathematical Analysis Society. The Hilbert Journal of Mathematical Analysis (Hilbert J. Math. Anal.) is published by Komunitas Analisis Matematika Indonesia (Kamindo). The Hilbert Journal of Mathematical Analysis is a peer-reviewed, open access international journal publishing original and high quality research papers that treat mathematical analysis, geometry, topology and all closely related topics. This journal particularly focuses on the main problems in the following, but not limited to, areas: Real Functions Measure and Integration Complex Functions (one and several variables) Potential Theory Special Functions Ordinary Differential Equations Partial Differential Equations Dynamical Systems and Ergodic Theory Sequence, Series and Summability Approximation and Expansion Harmonic Analysis (on Euclidean and Abstract Spaces) Integral Transform, Operational Calculus Integral Equations Functional Analysis Operator Theory Geometry Convex Geometry and Discrete Geometry Differential Geometry General Topology Global Analysis, Analysis on Manifold Probability Theory and Stochastic Processes Numerical Analysis
Arjuna Subject : Matematika - Analisis
Articles 30 Documents
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An equivalent norm of Herz spaces and its application to the Carleson operator Sawano, Yoshihiro
Hilbert Journal of Mathematical Analysis Vol. 3 No. 1 (2024): Hilbert J. Math. Anal.
Publisher : KOMUNITAS Analisis Matematika INDONESIA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62918/hjma.v3i1.29

Abstract

By establishing a new norm equivalence on Herz spaces using the Muckenhoupt class, the boundedness of the maximal modulated singular integral operators is established. This boundedness also boils down to the boundedness of the Carleson operator over the real line.  
General inequalities of the Hilbert integral type using the method of switching to polar coordinates Chesneau, Christophe
Hilbert Journal of Mathematical Analysis Vol. 3 No. 1 (2024): Hilbert J. Math. Anal.
Publisher : KOMUNITAS Analisis Matematika INDONESIA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62918/hjma.v3i1.30

Abstract

Various inequalities of the Hilbert integral type have been established in the literature using different methods. Among them, the classical Hilbert integral inequality was proved in an elegant way by David C. Ullrich in 2013. It consists in using the method of switching to polar coordinates after some thorough integral manipulations. Despite its effectiveness, this method seems to have been under-studied for more in the topic. In this paper we rehabilitate it somewhat and show how it can be used to prove new general inequalities of the Hilbert integral type, including some with multiple tuning parameters. Particular examples of interest are also discussed.
A new type of convergence in partial metric spaces Nuray, Fatih; Nuray Yıldırım, Elif
Hilbert Journal of Mathematical Analysis Vol. 3 No. 2 (2025): Hilbert J. Math. Anal.
Publisher : KOMUNITAS Analisis Matematika INDONESIA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62918/hjma.v3i2.31

Abstract

In this paper, we introduce the concept of deferred statistical convergence in partial metric spaces (pms), extending classical notions of statistical convergence and summability. We define deferred Cesaro summability and investigate its fundamental properties. Connections between statistical convergence and deferred Cesaro summability are explored, including inclusion relationships and strictness. Additionally, we establish conditions under which deferred summability implies statistical convergence and vice versa. Examples and theorems are provided to illustrate the applicability and relevance of these concepts in partial metric spaces.
Intermediate spaces on weak type discrete Morrey spaces Yudatama, Rizma; Hakim, Denny Ivanal
Hilbert Journal of Mathematical Analysis Vol. 3 No. 2 (2025): Hilbert J. Math. Anal.
Publisher : KOMUNITAS Analisis Matematika INDONESIA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62918/hjma.v3i2.33

Abstract

In this article we discuss inclusion between a discrete Morrey space and a weak discrete Morrey space as well as inclusion between two weak discrete Morrey spaces. By the inclusion properties of weak discrete Morrey spaces, we have intermediate spaces for the trivial case. Using the inclusion relation of discrete Morrey spaces and weak discrete Morrey spaces, we obtain that for the nontrivial case there is no weak discrete Morrey space between Banach pairs of weak discrete Morrey spaces except for the two weak discrete Morrey spaces itself.
Isoperimetric problems on n-sided prisms Ali, Amrizal Marwan; Hakim, Denny Ivanal
Hilbert Journal of Mathematical Analysis Vol. 3 No. 1 (2024): Hilbert J. Math. Anal.
Publisher : KOMUNITAS Analisis Matematika INDONESIA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62918/hjma.v3i1.36

Abstract

In two-dimensional figure, the isoperimetric problem refers to finding two-dimensional figure that will produce the largest area among several shapes with equal perimeter. This research extends the isoperimetric problem to finding three-dimensional shapes with maximum volume among those having equal surface area. Our main goal is to solve the isoperimetric problem for prisms with regular n-sided base, prisms with irregular n-sided base and cylinder. In this research, the discussion is limited to prisms with regular and irregular bases. Our problem is equivalent with the problem of finding the smallest surface area of a given three-dimensional figure with the same volume. We will use a geometric approachin our proof. we will see the relationship between isoperimetric problems in two dimensional figures and isoperimetric problems in three-dimensional figure. We obtain the results of the isoperimetric problem from two prisms with regular n-sided bases and a prism with regular m-sided bases with n≤m, two prisms with regular n-sided bases and a prism with circular bases (cylinder), and two prisms with regular n-sided bases and a prism with irregular n-sided bases.
Rate of convergence of Kantorovich operator sequences near L1([0, 1]) Abdul Karim Munir Aszari; Denny Ivanal Hakim
Hilbert Journal of Mathematical Analysis Vol. 3 No. 1 (2024): Hilbert J. Math. Anal.
Publisher : KOMUNITAS Analisis Matematika INDONESIA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62918/hjma.v3i1.37

Abstract

The study of the rate of convergence of Kantorovich operator sequences has predominantly focused on the Lp spaces for 1< p<infty, yet the behaviour near L1([0,1]) remains less understood, particularly as p approaches 1. To bridge this gap, we investigate the rate of convergence within the framework of the grand Lebesgue spaces Lp ([0,1]), which encompass all Lp ([0,1]) spaces for 1<p<infty but remain a subset of L1([0,1]). Our approach leverages the intrinsic properties of Lp ([0,1]) to derive new results on the convergence rate of Kantorovich operator sequences. Specifically, our objective is to demonstrate that Kantorovich operators exhibit a significant rate of convergence within this broader context, thereby providing insights applicable to the boundary behavior as p to 1. We will then apply these findings to alpha-Holder continuous functions to further understand the convergence rate of Kantorovich operator sequences in these settings. This combined approach suggests that functions with derivatives in Lp ([0,1]) exhibit specific convergence rates under Kantorovich operators.
An F-norm on sequences spaces Idris, Mochammad
Hilbert Journal of Mathematical Analysis Vol. 3 No. 1 (2024): Hilbert J. Math. Anal.
Publisher : KOMUNITAS Analisis Matematika INDONESIA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62918/hjma.v3i1.39

Abstract

On sequences spaces, we can choose a Young function that plays a role in determining their norm structure. In this article, we modify the Young function by replacing its convexity property with concavity to define the F-norm in these spaces. Furthermore, we explore the properties of the modified Young function. Additionally, we investigate the completeness of the space, allowing it to be classified as an F-space (Frechet space).
Inclusion between Bourgain-Morrey spaces and their weak types Pratama, Aria; Ivanal Hakim, Denny
Hilbert Journal of Mathematical Analysis Vol. 3 No. 2 (2025): Hilbert J. Math. Anal.
Publisher : KOMUNITAS Analisis Matematika INDONESIA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62918/hjma.v3i2.35

Abstract

This paper aims to explore the embedding relation between Bourgain-Morrey spaces and weak Bourgain-Morrey spaces. Bourgain-Morrey Spaces are important function spaces in harmonic analysis. In this article, we introduce weak Bourgain-Morrey spaces as certain generalization of weak Morrey spaces. We investigate the necessary and sufficient conditions for functions in weak Bourgain-Morrey spaces to also be elements in Bourgain-Morrey spaces, and vice versa. Our result are inclusion between weak Bourgain-Morrey spaces and inclusion of weak Bourgain- Morrey spaces into a certain Bourgain-Morrey spaces. These result generelize the inclusion result in Morrey spaces, weak Morrey spaces, and Bourgain- Morrey spaces.
Simplified computation of useful functions in linear canonical transform Bahri, Mawardi
Hilbert Journal of Mathematical Analysis Vol. 3 No. 2 (2025): Hilbert J. Math. Anal.
Publisher : KOMUNITAS Analisis Matematika INDONESIA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62918/hjma.v3i2.40

Abstract

The linear canonical transform is an extension of the usual Fourier transform because the Fourier transform is a special form of the linear canonical transform. It also is a valuable tool in signal analysis. Many essential properties of the Fourier transform can be transferred in the linear canonical Fourier domain with some changes. In this research paper, we first introduce the interesting connection between the linear canonical transform and Fourier transform. It is shown that the relation can be developed to efficiently evaluate Gaussian function in the linear canonical transform domain. Some examples of the Gaussian function in the linear canonical domain are also presented to illustrate the result.
A new integral inequality depending on the Lobachevskii function Chesneau, Christophe
Hilbert Journal of Mathematical Analysis Vol. 3 No. 2 (2025): Hilbert J. Math. Anal.
Publisher : KOMUNITAS Analisis Matematika INDONESIA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62918/hjma.v3i2.38

Abstract

This paper investigates a new logarithmic variant of the Hilbert integral inequality, beyond the standard homogeneous assumption. To this end, several theorems and propositions are proved, each of which gives new integral inequalities of independent interest. Remarkably, the Lobachevskii function appears quite naturally in some proofs, and forms an important part of the upper bound obtained. Several sharp examples are developed and discussed. A brief overview of the Lobachevskii function is given in the appendix.

Page 3 of 3 | Total Record : 30

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