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On the function spaces of general weights
https://doi.org/10.26907/0021-3446-2025-12-40-70
Abstract
The aim of this paper is twofold. First, we establish the ^-transform characterizations of the Besov spaces Bp,q (Rn, {tk}) and the Triebel-Lizorkin spaces Fp,q (Rn, {tk}) for q = to, in the sense of Frazier and Jawerth. Second, under some suitable assumptions on a padmissible weight sequence {tk}, we prove that Ap,q (Rn, {tk }) = Ap,q (Rn,tj), j ϵ Z, in the sense of equivalent quasi-norms, with A ϵ {B,F}. Moreover, we find a necessary and sufficient condition for the coincidence of the spaces Ap,q (Rn,ti), i ϵ {1, 2}.
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For citations:
Drihem D. On the function spaces of general weights. Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika. 2025;(12):40-70. (In Russ.) https://doi.org/10.26907/0021-3446-2025-12-40-70
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