Maximal Operators Associated With Walsh-Paley Systems on Dyadic Hardy Spaces

Ushangi Goginava; Nacima Memić; Farrukh Mukhamemdov

doi:10.1002/mma.10841

Maximal Operators Associated With Walsh-Paley Systems on Dyadic Hardy Spaces

Ushangi Goginava
, Nacima Memić
, Farrukh Mukhamemdov

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

The concept of a critical point of the maximum operator (Formula presented.) associated with the Walsh-Paley system is the focus of this study. Namely, a point (Formula presented.) is called critical with respect to (Formula presented.), if (Formula presented.) is bounded from (Formula presented.) to (Formula presented.), for all (Formula presented.) and it is not bounded from (Formula presented.) to (Formula presented.). The main result of the this paper states that if (Formula presented.) serves as a critical point, then (Formula presented.) is bounded from (Formula presented.) to (Formula presented.). Additionally, we demonstrate that for every value (Formula presented.), there exists a sequence of operators even over subset (Formula presented.) that is not uniformly bounded from (Formula presented.) to (Formula presented.).

Original language	English
Pages (from-to)	9770-9777
Number of pages	8
Journal	Mathematical Methods in the Applied Sciences
Volume	48
Issue number	9
DOIs	https://doi.org/10.1002/mma.10841
Publication status	Published - Jun 2025

Keywords

Hardy space
Walsh system
sequence of operators
uniform boundedness

ASJC Scopus subject areas

General Mathematics
General Engineering

Access to Document

10.1002/mma.10841

Cite this

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title = "Maximal Operators Associated With Walsh-Paley Systems on Dyadic Hardy Spaces",

abstract = "The concept of a critical point of the maximum operator (Formula presented.) associated with the Walsh-Paley system is the focus of this study. Namely, a point (Formula presented.) is called critical with respect to (Formula presented.), if (Formula presented.) is bounded from (Formula presented.) to (Formula presented.), for all (Formula presented.) and it is not bounded from (Formula presented.) to (Formula presented.). The main result of the this paper states that if (Formula presented.) serves as a critical point, then (Formula presented.) is bounded from (Formula presented.) to (Formula presented.). Additionally, we demonstrate that for every value (Formula presented.), there exists a sequence of operators even over subset (Formula presented.) that is not uniformly bounded from (Formula presented.) to (Formula presented.).",

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author = "Ushangi Goginava and Nacima Memi{\'c} and Farrukh Mukhamemdov",

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language = "English",

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T1 - Maximal Operators Associated With Walsh-Paley Systems on Dyadic Hardy Spaces

AU - Goginava, Ushangi

AU - Memić, Nacima

AU - Mukhamemdov, Farrukh

PY - 2025/6

Y1 - 2025/6

N2 - The concept of a critical point of the maximum operator (Formula presented.) associated with the Walsh-Paley system is the focus of this study. Namely, a point (Formula presented.) is called critical with respect to (Formula presented.), if (Formula presented.) is bounded from (Formula presented.) to (Formula presented.), for all (Formula presented.) and it is not bounded from (Formula presented.) to (Formula presented.). The main result of the this paper states that if (Formula presented.) serves as a critical point, then (Formula presented.) is bounded from (Formula presented.) to (Formula presented.). Additionally, we demonstrate that for every value (Formula presented.), there exists a sequence of operators even over subset (Formula presented.) that is not uniformly bounded from (Formula presented.) to (Formula presented.).

AB - The concept of a critical point of the maximum operator (Formula presented.) associated with the Walsh-Paley system is the focus of this study. Namely, a point (Formula presented.) is called critical with respect to (Formula presented.), if (Formula presented.) is bounded from (Formula presented.) to (Formula presented.), for all (Formula presented.) and it is not bounded from (Formula presented.) to (Formula presented.). The main result of the this paper states that if (Formula presented.) serves as a critical point, then (Formula presented.) is bounded from (Formula presented.) to (Formula presented.). Additionally, we demonstrate that for every value (Formula presented.), there exists a sequence of operators even over subset (Formula presented.) that is not uniformly bounded from (Formula presented.) to (Formula presented.).

KW - Hardy space

KW - Walsh system

KW - sequence of operators

KW - uniform boundedness

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Maximal Operators Associated With Walsh-Paley Systems on Dyadic Hardy Spaces

Abstract

Keywords

ASJC Scopus subject areas

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