Standard

New Characterization of -Adic Herz Spaces with Applications to the Vector-valued Maximal Inequality of Fefferman–Stein Type. / Sawano, Y.

In: Lobachevskii Journal of Mathematics, Vol. 45, No. 12, 26.03.2025, p. 6201-6208.

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

Harvard

Sawano, Y 2025, 'New Characterization of -Adic Herz Spaces with Applications to the Vector-valued Maximal Inequality of Fefferman–Stein Type', Lobachevskii Journal of Mathematics, vol. 45, no. 12, pp. 6201-6208. https://doi.org/10.1134/S1995080224607641

APA

Sawano, Y. (2025). New Characterization of -Adic Herz Spaces with Applications to the Vector-valued Maximal Inequality of Fefferman–Stein Type. Lobachevskii Journal of Mathematics, 45(12), 6201-6208. https://doi.org/10.1134/S1995080224607641

Vancouver

Sawano Y. New Characterization of -Adic Herz Spaces with Applications to the Vector-valued Maximal Inequality of Fefferman–Stein Type. Lobachevskii Journal of Mathematics. 2025 Mar 26;45(12):6201-6208. doi: 10.1134/S1995080224607641

Author

Sawano, Y. / New Characterization of -Adic Herz Spaces with Applications to the Vector-valued Maximal Inequality of Fefferman–Stein Type. In: Lobachevskii Journal of Mathematics. 2025 ; Vol. 45, No. 12. pp. 6201-6208.

BibTeX

@article{4cf77d325a734ef192a0dd5d130942d8,
title = "New Characterization of -Adic Herz Spaces with Applications to the Vector-valued Maximal Inequality of Fefferman–Stein Type",
abstract = "Abstract: Recently, Fu, Wu, and Lu defined -adic Herz spaces. The main goal of this paper is to give a simple proof of the vector-valued maximal inequality of Fefferman–Stein type for -adic Herz spaces. The main ingredient is the new norm equivalence that is adapted to the Muckenhoupt class for the -dimensional -adic space. A review of the -dimensional -adic space is given after the main theorem is stated. This review covers the aspect of measure theory over the -dimensional -adic space. After the proof of this main result, some other possibilities for extensions are discussed. This includes i) weak function spaces together with an application, ii) Hardy operators and iii) variable exponents. Since the theory of weights on the class of variable Lebesgue spaces is missing, the investigation of variable exponents is left for future works. The method used in this paper is simple and promises applications to various situations.",
keywords = "-adic, Herz spaces, maximal operator, vector-valued, weights",
author = "Y. Sawano",
note = "Yoshihiro Sawano is supported by Japan Society for the Promotion of Science, Grant Number: 23K03156.",
year = "2025",
month = mar,
day = "26",
doi = "10.1134/S1995080224607641",
language = "English",
volume = "45",
pages = "6201--6208",
journal = "Lobachevskii Journal of Mathematics",
issn = "1995-0802",
publisher = "ФГБУ {"}Издательство {"}Наука{"}",
number = "12",

}

RIS

TY - JOUR

T1 - New Characterization of -Adic Herz Spaces with Applications to the Vector-valued Maximal Inequality of Fefferman–Stein Type

AU - Sawano, Y.

N1 - Yoshihiro Sawano is supported by Japan Society for the Promotion of Science, Grant Number: 23K03156.

PY - 2025/3/26

Y1 - 2025/3/26

N2 - Abstract: Recently, Fu, Wu, and Lu defined -adic Herz spaces. The main goal of this paper is to give a simple proof of the vector-valued maximal inequality of Fefferman–Stein type for -adic Herz spaces. The main ingredient is the new norm equivalence that is adapted to the Muckenhoupt class for the -dimensional -adic space. A review of the -dimensional -adic space is given after the main theorem is stated. This review covers the aspect of measure theory over the -dimensional -adic space. After the proof of this main result, some other possibilities for extensions are discussed. This includes i) weak function spaces together with an application, ii) Hardy operators and iii) variable exponents. Since the theory of weights on the class of variable Lebesgue spaces is missing, the investigation of variable exponents is left for future works. The method used in this paper is simple and promises applications to various situations.

AB - Abstract: Recently, Fu, Wu, and Lu defined -adic Herz spaces. The main goal of this paper is to give a simple proof of the vector-valued maximal inequality of Fefferman–Stein type for -adic Herz spaces. The main ingredient is the new norm equivalence that is adapted to the Muckenhoupt class for the -dimensional -adic space. A review of the -dimensional -adic space is given after the main theorem is stated. This review covers the aspect of measure theory over the -dimensional -adic space. After the proof of this main result, some other possibilities for extensions are discussed. This includes i) weak function spaces together with an application, ii) Hardy operators and iii) variable exponents. Since the theory of weights on the class of variable Lebesgue spaces is missing, the investigation of variable exponents is left for future works. The method used in this paper is simple and promises applications to various situations.

KW - -adic

KW - Herz spaces

KW - maximal operator

KW - vector-valued

KW - weights

UR - https://www.mendeley.com/catalogue/ca25f08f-5c81-3a73-8033-78953c10bab8/

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-105001502355&origin=inward&txGid=f4be31645e716b468e4dc7ebff103089

U2 - 10.1134/S1995080224607641

DO - 10.1134/S1995080224607641

M3 - Article

VL - 45

SP - 6201

EP - 6208

JO - Lobachevskii Journal of Mathematics

JF - Lobachevskii Journal of Mathematics

SN - 1995-0802

IS - 12

ER -

ID: 65163477