Calderón-Zygmund operators on compact Lie groupes.
Oscillatory Integrals and Atoms on the Unit sphere.
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.
Multiplier transformations on spaces
The authors obtain some multiplier theorems on spaces analogous to the classical multiplier theorems of de Leeuw. The main result is that a multiplier operator is bounded on if and only if the restriction is an bounded multiplier uniformly for ε>0, where Λ is the integer lattice in .
Weighted weak type (1,1) estimates for singular integrals and Littlewood-Paley functions
We prove some weighted weak type (1,1) inequalities for certain singular integrals and Littlewood-Paley functions.
L boundedness of a singular integral operator.
In this paper we study a singular integral operator T with rough kernel. This operator has singularity along sets of the form {x = Q(|y|)y'}, where Q(t) is a polynomial satisfying Q(0) = 0. We prove that T is a bounded operator in the space L2(Rn), n ≥ 2, and this bound is independent of the coefficients of Q(t). We also obtain certain Hardy type inequalities related to this operator.
Optimal boundedness of central oscillating multipliers on compact Lie groups
Fefferman-Stein, Wainger and Sjölin proved optimal boundedness for certain oscillating multipliers on . In this article, we prove an analogue of their result on a compact Lie group.
Oscillatory kernels in certain Hardy-type spaces
We consider a convolution operator Tf = p.v. Ω ⁎ f with , where K(x) is an (n,β) kernel near the origin and an (α,β), α ≥ n, kernel away from the origin; h(x) is a real-valued function on . We give a criterion for such an operator to be bounded from the space into itself.
The method of rotation and Marcinkiewicz integrals on product domains
We give some rather weak sufficient condition for boundedness of the Marcinkiewicz integral operator on the product spaces (1 < p < ∞), which improves and extends some known results.
Regularity of some nonlinear quantities on superharmonic functions in local Herz-type Hardy spaces.
In this paper, the authors introduce a kind of local Hardy spaces in R associated with the local Herz spaces. Then the authors investigate the regularity in these local Hardy spaces of some nonlinear quantities on superharmonic functions on R. The main results of the authors extend the corresponding results of Evans and Müller in a recent paper.
Hardy spaces on compact Lie groups
Hausdorff operator on Morrey spaces and Campanato spaces
We study the high-dimensional Hausdorff operators on the Morrey space and on the Campanato space. We establish their sharp boundedness on these spaces. Particularly, our results solve an open question posted by E. Liflyand (2013).
Regularity in Morrey spaces of strong solutions to nondivergence elliptic equations with VMO coefficients.
On an extension of singular integrals along manifolds of finite type.
The Kobayashi metric of a complex ellipsoid in .
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