Boundedness of Sublinear Operators with Rough Kernels on Weighted Morrey Spaces

Boundedness criteria for commutators of some sublinear operators in weighted Morrey spaces

In this paper, we obtain bounded criteria on certain weighted Morrey spaces for the commutators generalized by some sublinear integral operators and weighted Lipschitz functions. We also present bounded criteria for commutators generalized by such sublinear integral operators and weighted BMO function on the weighted Morrey spaces. As applications, our results yield the same bounded criteria fo...

Weighted Anisotropic Product Hardy Spaces and Boundedness of Sublinear Operators

Let A1 and A2 be expansive dilations, respectively, on R n and R. Let ~ A ≡ (A1, A2) and Ap( ~ A) be the class of product Muckenhoupt weights on R × R for p ∈ (1, ∞]. When p ∈ (1, ∞) and w ∈ Ap( ~ A), the authors characterize the weighted Lebesgue space L w (R × R) via the anisotropic Lusin-area function associated with ~ A. When p ∈ (0, 1], w ∈ A∞( ~ A), the authors introduce the weighted anis...

Boundedness of Sublinear Operators on the Homogeneous Herz Spaces

Boundedness of Rough Integral Operators on Triebel-lizorkin Spaces

We prove the boundedness of several classes of rough integral operators on Triebel-Lizorkin spaces. Our results represent improvements as well as natural extensions of many previously known results. 2010 Mathematics Subject Classification: Primary: 42B20; Secondary: 42B15, 42B25.

On the Boundedness of Classical Operators on Weighted Lorentz Spaces

Conditions on weights u(·), v(·) are given so that a classical operator T sends the weighted Lorentz space Lrs(vdx) into Lpq(udx). Here T is either a fractional maximal operator Mα or a fractional integral operator Iα or a Calderón–Zygmund operator. A characterization of this boundedness is obtained for Mα and Iα when the weights have some usual properties and max(r, s) ≤ min(p, q). § 0. Introd...