On the function spaces of general weights

2022/12/07 by Drihem, Douadi
#42B35 #FOS: Mathematics #Functional Analysis (math.FA) #Primary: 42B25 #secondary: 46E35

paper · doi:10.48550/arxiv.2212.03509

Abstract

The aim of this paper is twofold. Firstly, we chatacterize the Besov spaces B_p,q(ℝⁿ,\t_k\) and the Triebel-Lizorkin spaces F_p,q(ℝⁿ,\t_k\) for q=∞ . Secondly, under some suitable assumptions on the p-admissible weight sequence \t_k\, we prove that A_p,q(ℝⁿ,\t_k\)=A_p,q(ℝ ⁿ,t_j), j∈ ℤ, in the sense of equivalent quasi-norms, with A ∈ \B,F\. Moreover, we find a necessary and sufficient conditions for the coincidence of the spaces A_p,q(ℝⁿ,t_i),i∈ \1,2\.

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