Boundedness of fractional integrals on special John–Nirenberg–Campanato and Hardy-type spaces via congruent cubes

Boundedness of Singular Integrals in Weighted Anisotropic Product Hardy Spaces

Let Ai for i = 1, 2 be an expansive dilation, respectively, on R n and R and ~ A ≡ (A1, A2). Denote by A∞(R × R; ~ A) the class of Muckenhoupt weights associated with ~ A. The authors introduce a class of anisotropic singular integrals on R×R, whose kernels are adapted to ~ A in the sense of Bownik and have vanishing moments defined via bump functions in the sense of Stein. Then the authors est...

Boundedness of Marcinkiewicz integrals with rough kernels on Musielak-Orlicz Hardy spaces

Let [Formula: see text] satisfy that [Formula: see text], for any given [Formula: see text], is an Orlicz function and [Formula: see text] is a Muckenhoupt [Formula: see text] weight uniformly in [Formula: see text]. The Musielak-Orlicz Hardy space [Formula: see text] is defined to be the set of all tempered distributions such that their grand maximal functions belong to the Musielak-Orlicz spa...

Boundedness on Hardy-Sobolev Spaces for Hypersingular Marcinkiewicz Integrals with Variable Kernels

Atomic Decomposition and Boundedness Criterion of Operators on Multi-parameter Hardy Spaces of Homogeneous Type

The main purpose of this paper is to derive a new (p, q)-atomic decomposition on the multi-parameter Hardy space H(X1 ×X2) for 0 < p0 < p ≤ 1 for some p0 and all 1 < q < ∞, where X1 × X2 is the product of two spaces of homogeneous type in the sense of Coifman and Weiss. This decomposition converges in both L(X1 × X2) (for 1 < q < ∞) and Hardy space H(X1 × X2) (for 0 < p ≤ 1). As an application,...

Boundedness for Multilinear Marcinkiewicz Operators on Certain Hardy Spaces

The boundedness for the multilinear Marcinkiewicz operators on certain Hardy and Herz-Hardy spaces are obtained.