In this paper, we investigate several two-parameter weak Orlicz–Hardy martingale spaces generated by the $p$-convex and $q$-concave functions, establish their atomic decomposition theorems. Using decomposition, obtain a sufficient condition for boundedness of sublinear operator defined on spaces. Furthermore, dual are considered.

We prove continuity results for Fourier integral operators with symbols in modulation spaces, acting between modulation spaces. The phase functions belong to a class of nondegenerate generalized quadratic forms that includes Schrödinger propagators and pseudodifferential operators. As a byproduct we obtain a characterization of all exponents p, q, r 1 , r 2 , t 1 , t 2 ∈ [1, ∞] of modulation sp...

Keywords: Boundary value problems Differential-operator equations Banach-valued Besov spaces Operator-valued multipliers Interpolation of Banach spaces a b s t r a c t The boundary value problems for linear and nonlinear degenerate differential-operator equations in Banach-valued Besov spaces are studied. Several conditions for the separability of linear elliptic problems are given. Moreover, t...

Basis properties of exponential and trigonometric systems in grand Lebesgue spaces $ L_{p)} (-\pi,\pi) are studied. Based on a shift operator, we consider the subspace $G_{p)} (-\pi,\pi)$ space $, where continuous functions dense, boundedness singular operator this is proved. We establish basicity system \{{e^{int}}\}_{n\in Z}$ for \{{\sin{nt}}\}_{n\in N }$ \{{\cos{nt}}\}_{n\in N_0}$ (0,\pi)$.

The purpose of this paper is to study the boundedness in the context of Triebel-Lizorkin spaces for some multilinear operators related to certain convolution operators. The operators include Littlewood-Paley operator, Marcinkiewicz integral, and Bochner-Riesz operator. 1. Introduction. Let T be a Calderon-Zygmund operator. A well-known result of Coif-man et al. [6] states that the commutator [b...