Naslov
The weighted discrete Gehring classes, Muckenhoupt classes and their basic properties

Autori
Saker, Samir ; Krnić, Mario

Izvornik
Proceedings of the American Mathematical Society (0002-9939) 149 (2021), 1; 231-243

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
discrete Gehring class, discrete Muckenhoupt class, self-improving property, harmonic analysis

Sažetak
The main objective of this paper is a study of the structure and basic properties of the weighted discrete Gehring classes, as well as the study of relationship between discrete Muckenhoupt and Gehring classes. First, we prove that the weighted discrete Muckenhoupt class \mathcal{; ; A}; ; _{; ; \lambda }; ; ^{; ; 1}; ; (C)$, $C>1$, consisting of nonincreasing sequences, belongs to the weighted discrete Gehring class $\mathcal{; ; G}; ; % _{; ; \lambda }; ; ^{; ; p}; ; (A)$, by giving explicit values of exponent $p$ and constant $A$. Next, we prove the self-improving property of the weighted Gehring class $\mathcal{; ; G}; ; _{; ; \lambda }; ; ^{; ; p}; ; ({; ; K)}; ; $, $p>1$, $K>1$, consisting of nonincreasing sequences. The exponent and constant of transition are explicitly given. Finally, utilizing the self-improving property of the weighted Gehring class, we also derive the self-improving property of a discrete Muckenhoupt class $\mathcal{; ; A}; ; ^{; ; p}; ; (C)$, $p>1$, $C>1$, with exact values of exponent and constant of transition.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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