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Al Azhary Masta

Publications and source records attributed to Al Azhary Masta.

9 recordsLinked to original sources
arXiv2026

Bounded Multilinear Functionals and Multicontinuous Functions on n-Normed Spaces

In this paper, we introduced some notions on the n-Normed Spaces. Those are bounded k-linear (or multilinear) functionals and k-continuous (or multicontinuous) functions with k \in \mathbb{N}. We defined k-linear functionals under several types of boundedness, and constructed the corresponding dual spaces based on each type of boundedness. We then proved that these types of boundedness are actually equivalent. This means the boundedness of a multilinear functional can be verified using any of the equivalent notions of boundedness that we defined earlier. The equivalent also implies that all of the resulting dual spaces are identical as a set. We also defined two norms on the dual spaces and showed that both norms are equivalent. Moreover, we gave some examples of bounded k-linear functionals on an n-normed space and calculated their norms with respect to the types of boundedness. We also defined a new notion of k-continuous function in n-normed spaces. Then we gave a relation between the bounded k-linear functional and k-continuous function in n-normed spaces.

math.FA↗
arXiv2025

Generalized Discrete Orlicz-Morrey Spaces

The Orlicz-Morrey spaces, which were introduced through the research of Nakai in 2006, are a generalization and combination of Orlicz and Morrey spaces. There are two types of Orlicz-Morrey spaces, such as continuous Orlicz-Morrey spaces and discrete Orlicz-Morrey spaces. Some properties that apply to Orlicz-Morrey spaces have been studied correspondingly to discrete Orlicz-Morrey spaces. The objectives of the study are to construct generalized discrete Orlicz-Morrey spaces by substituting a Young function with \emph{s}-Young function. Furthermore, The purpose of this study is to see the validity of the properties of the discrete Orlicz-Morrey spaces to the generality of the discrete Orlicz-Morrey spaces. The method in this research draws on the definitions and properties of the discrete Orlicz-Morrey spaces of the previous study and applies the \emph{s}-Young function to the new Orlicz-Morrey spaces. As a result, this study concludes that generalized discrete Orlicz-Morrey spaces reduce to discrete Orlicz-Morrey spaces when \emph{s} is equal to 1. Furthermore, due to the characteristics of the \emph{s}-Young function, some properties of discrete Orlicz-Morrey spaces are preserved in generalized discrete Orlicz-Morrey spaces.

math.FA↗
arXiv2018

A Note on Inclusion Properties of Weighted Orlicz Spaces

In this paper we present sufficient and necessary conditions for inclusion relation between two weighted Orlicz spaces which complete the Osançliol result in 2014. One of the keys to prove our results is to use the norm of the characteristic functions of the balls in $\mathbb{R}^n$.

math.FA↗
arXiv2018

Generalized Hölder's Inequality in Orlicz Spaces

Orlicz spaces are generalizations of Lebesgue spaces. The sufficient and necessary conditions for generalized Hölder's inequality in Lebesgue spaces and in weak Lebesgue spaces are well known. The aim of this paper is to present sufficient and necessary conditions for generalized Hölder's inequality in Orlicz spaces and in weak Orlicz spaces, which are obtained through estimates for characteristic functions of balls in $\R^n$.

math.FA↗
arXiv2018

Third Version of Weak Orlicz--Morrey Spaces and Its Inclusion Properties

Orlicz--Morrey spaces are generalizations of Orlicz spaces and Morrey spaces which were first introduced by Nakai. There are three versions of Orlicz--Morrey spaces, i.e: Nakai's (2004), Sawano--Sugano--Tanaka's (2012), and Deringoz--Guliyev--Samko's (2014) versions. On this article we will discuss the third version of weak Orlicz--Morrey space which is seen as an enlargement of third version of (strong) Orlicz--Morrey space. Similar to its first version and second version, the third version of weak Orlicz-Morrey space is considered as a generalization of weak Orlicz spaces, weak Morrey spaces, and generalized weak Morrey spaces. In this study, we will investigate some properties of the third version of weak Orlicz--Morrey spaces, especially the sufficient and necessary conditions for inclusion relations between two these spaces. One of the keys to get our result is to estimate the quasi-norm of characteristics function of open balls in $\mathbb{R}^n$.

math.FA↗
arXiv2018

Generalized Hölder's inequality on Morrey spaces

The aim of this paper is to present necessary and sufficient conditions for generalized Hölder's inequality on generalized Morrey spaces. We also obtain similar results on weak Morrey spaces and on generalized weak Morrey spaces. The necessary and sufficient conditions for the generalized Hölder's inequality on these spaces are obtained through estimates for characteristic functions of balls in $\mathbb{R}^d$.

math.AP↗
arXiv2017

Inclusion Properties of Weighted Weak Orlicz Spaces

In this paper we discuss the structure of weighted weak Lebesgue spaces and weighted weak Orlicz spaces on $\mathbb{R}^n$. First, we present sufficient and necessary conditions for inclusion relation between weighted weak Lebesgue spaces. Next, we also obtain similar results on weighted weak Orlicz spaces. One of the keys to prove our results is to use the norm of the characteristic functions of the balls in $\mathbb{R}^n$.

math.FA↗
arXiv2016

Inclusion properties of Orlicz and weak Orlicz spaces

In this paper we discuss the structure of Orlicz spaces and weak Orlicz spaces on $\mathbb{R}^n$. We obtain some necessary and sufficient conditions for the inclusion property of these spaces. One of the keys is to compute the norm of the characteristic functions of the balls in $\mathbb{R}^n$.

math.FA↗