Boundedness criterion for multilinear oscillatory integrals with rough kernels
We study a multilinear oscillatory integral with rough kernel and establish a boundedness criterion.
Boundedness for a bilinear model sum operator on ℝⁿ
The purpose of this article is to obtain a multidimensional extension of Lacey and Thiele's result on the boundedness of a model sum which plays a crucial role in the boundedness of the bilinear Hilbert transform in one dimension. This proof is a simplification of the original proof of Lacey and Thiele modeled after the presentation of Bilyk and Grafakos.
Boundedness for commutators of Littlewood-Paley operators on some Hardy spaces.
Boundedness for multilinear commutator of integral operator on Hardy and Herz-Hardy spaces.
Boundedness for multilinear commutator of Littlewood--Paley operator on Hardy and Herz--Hardy spaces.
Boundedness for multilinear commutator of Littlewood-Paley operator on Hardy and Herz-Hardy spaces.
Boundedness for multilinear commutator of Littlewood-Paley operator on Hardy and Herz-Hardy spaces.
Boundedness for multilinear Littlewood-Paley operators on Hardy and Herz-Hardy spaces.
Boundedness for multilinear Marcinkiewicz operators on certain Hardy spaces.
Boundedness for multilinear operators of multiplier operators on Triebel-Lizorkin and Lebesgue spaces.
Boundedness for multilinear singular integral operators on Morrey spaces.
Boundedness from to of Riesz transforms on a Lie group of exponential growth
Let be the Lie group endowed with the Riemannian symmetric space structure. Let be a distinguished basis of left-invariant vector fields of the Lie algebra of and define the Laplacian . In this paper we consider the first order Riesz transforms and , for . We prove that the operators , but not the , are bounded from the Hardy space to . We also show that the second-order Riesz transforms are bounded from to , while the transforms and , for , are not.
Boundedness of certain oscillatory singular integrals
We prove the and boundedness of oscillatory singular integral operators defined by Tf = p.v.Ω∗f, where , K(x) is a Calderón-Zygmund kernel, and Φ satisfies certain growth conditions.
Boundedness of commutators of an oscillatory integral operator
We obtain a necessary and sufficient condition for boundedness of commutators of certain oscillatory integral operators and Lipschitz functions.
Boundedness of commutators of singular and potential operators in generalized grand Morrey spaces and some applications
In the setting of spaces of homogeneous type, it is shown that the commutator of Calderón-Zygmund type operators as well as the commutator of a potential operator with a BMO function are bounded in a generalized grand Morrey space. Interior estimates for solutions of elliptic equations are also given in the framework of generalized grand Morrey spaces.
Boundedness of commutators of strongly singular convolution operators on Herz-type spaces
The author investigates the boundedness of the higher order commutator of strongly singular convolution operator, , on Herz spaces and , and on a new class of Herz-type Hardy spaces and , where 0 < p ≤ 1 < q < ∞, α = n(1-1/q) and b ∈ BMO(ℝⁿ).
Boundedness of higher order commutators of oscillatory singular integrals with rough kernels
The author studies the commutators generated by a suitable function a(x) on ℝⁿ and the oscillatory singular integral with rough kernel Ω(x)|x|ⁿ and polynomial phase, where Ω is homogeneous of degree zero on ℝⁿ, and a(x) is a BMO function or a Lipschitz function. Some mapping properties of these higher order commutators on , which are essential improvements of some well known results, are given.
Boundedness of multilinear commutator of singular integral in Morrey spaces on homogeneous spaces.
Boundedness of one-sided fractional integrals in the one-sided Calderón-Hardy spaces
In this paper we study the mapping properties of the one-sided fractional integrals in the Calderón-Hardy spaces for , and . Specifically, we show that, for suitable values of and , if (Sawyer’s classes of weights) then the one-sided fractional integral can be extended to a bounded operator from to . The result is a consequence of the pointwise inequality where denotes the Calderón maximal function.