Intermediate spaces between ∧2≤τ<∞ Lτ and L∞

[摘要] In this paper we introduce an intermediate space L-psi,L-lambda(T) between boolean AND(tau >= 2) L-tau (T) and L-infinity (T), where L-tau (T) are the L-tau-subspaces of a nonatomic finite measure space {T, Sigma, mu}, and study its properties. In particular, this space is Banach and rearrangement-invariant with respect to the measure mu. Our main result states that under some conditions L-psi,L-lambda (T) coincides with a special Marcinkiewicz space. In addition, we obtain Zygmund-type weak and integral estimates for functions from L-psi,L-lambda (T) and apply them to estimate the norms of the conjugate, Fourier, and Littlewood-Paley operators from L-infinity(T) to L-psi,L-lambda(T), where T is the unit circle in C. Relationships between L-psi,L-lambda(T) and BMO(T) are discussed as well. (C) 2013 Elsevier Inc. All rights reserved.

[发布日期] 2013-12-15

[关键词] Intermediate space;Rearrangement;Marcinkiewicz space;BMO;Zygmund-type inequalities;Conjugate operator;Littlewood-Paley operator