Boundedness of the θ-type Calderón-Zygmund Operators on Weighted Herz-type Hardy Spaces

In this paper,we will discuss the boundedness of θ-type Calderón-Zygmund operator on weighted Herz-type Hardy spaces.     

L~p Boundedness of Commutators of Calderón-Zygmund Singular Integral Operators

本文证明了当ｂ∈ＢＭＯ时，具有弱核的ＣａｌｄｅｒóｎＺｙｇｍｕｎｄ奇异积分算子的交换子［ｂ，Ｔ］ｆ＝ｂＴ（ｆ）－Ｔ（ｂｆ）是Ｌｐ（１＜ｐ＜∞）有界的．一个等价的命题是双线性算子ｇＴ（ｆ）－ｆＴ（ｇ）∈Ｈ１，只要ｆ∈Ｌｐ，ｇ∈Ｌｑ，１＜ｐ＜∞，１ｐ＋１ｑ＝１．     

The Boundedness of Calderón-Zygmund Operators by Wavelet Characterization

This article deals with the boundedness properties of Calderón-Zygmund operators on Hardy spaces Hp(Rn). We use wavelet characterization of Hp(Rn) to show that a Calderón-Zygmund operator T with T*1 = 0 is bounded on Hp(Rn), n/n+ε p ≤ 1, where ε is the regular exponent of kernel of T . This approach can be applied to the boundedness of operators on certain Hardy spaces without atomic decomposition or molecular characterization.     

Weak Type Weighted Inequalities for the Commutators of the Multilinear Calderón-Zygmund Operators

For the commutators of multilinear Calderón-Zygmund singular integral operators with B MO functions, the weak type weighted norm inequalities with respect to A_(→P) weights are obtained.     

Multilinear Commutators of θ-Type Calderón-Zygmund Operators on Non-Homogeneous Metric Measure Spaces

In this paper, the boundedness in Lebesgue spaces of commutators and multilinear commutators generated by θ-type Calderón-Zygmund operators with RB MO(μ) functions on non-homogeneous metric measure spaces is obtained.     

Bilinear Square Functions and Vector-Valued Calderón-Zygmund Operators

Boundedness results for bilinear square functions and vector-valued operators on products of Lebesgue, Sobolev, and other spaces of smooth functions are presented. Bilinear vector-valued Calderón-Zygmund operators are introduced and used to obtain bounds for the optimal range of estimates in target Lebesgue spaces including exponents smaller than one.     

Commutators of sublinear operators generated by Calderón-Zygmund operator on generalized weighted Morrey spaces

In this paper, the boundedness of a large class of sublinear commutator operators T _b generated by a Calderón-Zygmund type operator on a generalized weighted Morrey spaces \({M_{p,\varphi }}(w)\) with the weight function w belonging to Muckenhoupt’s class A _p is studied. When 1 < p < ∞ and b ∈ BMO, sufficient conditions on the pair (φ ₁, φ ₂) which ensure the boundedness of the operator T _b from \({M_{p,\varphi 1}}(w)\) to \({M_{p,\varphi 2}}(w)\) are found. In all cases the conditions for the boundedness of T _b are given in terms of Zygmund-type integral inequalities on (φ ₁, φ ₂), which do not require any assumption on monotonicity of φ ₁(x, r), φ ₂(x, r) in r. Then these results are applied to several particular operators such as the pseudo-differential operators, Littlewood-Paley operator, Marcinkiewicz operator and Bochner-Riesz operator.     

Multilinear Calderón-Zygmund Operator on Products of Hardy Spaces

In this paper, the authors establish the boundedness of the multilinear Calderón-Zygmund operator from products of Hardy spaces into Hardy spaces.     

Multi-weight, Weighted Weak Type Estimates for the Multilinear Calderón-Zygmund Operators

Let m be an integer and T be an m-linear Calderón-Zygmund operator, u, v1,..., vm be weights. In this paper, the authors give some sufficient conditions on the weights (u, vk) with 1 ≤ k ≤ m, such that T is bounded from Lp1(Rn, v1) × ··· × Lpm(Rn, vm) to Lp,∞(Rn, u).     

The algebra of Calderón-Zygmund kernels on a homogeneous group is inverse-closed

We show that the subalgebra of convolution operators with Calderón-Zygmund kernels on a homogeneous group G is inverse-closed in the algebra of all bounded linear operators on the Hilbert space L ²(G). The main tool used is a symbolic calculus, where the convolution of distributions on the group is translated via the abelian Fourier transform into a “twisted product” of symbols on the dual to the Lie algebra g of G.     

Calderón-Zygmund operators with kernels of Dini’s type on generalized weighted variable exponent Morrey spaces

Positivity - Let T be a Calderón-Zygmund operator of type $$omega $$ with $$omega (t)$$ being nondecreasing and satisfying a kind of Dini’s type condition and let $$T_{vec {b}}$$ be...     

Compactness of Product Operators on the Bergman Space

In this paper, we study the compactness of the product of a composition operator with another one＇s adjoint on the Bergman space. Some necessary and sufficient conditions for such operators to be compact are given.     

A Geometric Approach to the Calderón-Zygmund Estimates

In this note, we will show a new proof of the classical Calderón-Zygmund estimates established in [7] 1952. The estimates are among the fundamental estimates for elliptic equations. Parabolic equations are also considered.     

Musielak-Orlicz-Bumps and Bloom Type Estimates for Commutators of Calderón-Zygmund and Fractional Integral Operators on Generalized Zygmund Spaces Via Sparse Operators

Analysis Mathematica - We study continuity properties for commutators of Calderón-Zygmund and fractional integral operators between generalized Zygmund spaces of L log L type, in the variable...     

Boundedness of Commutators of θ-Type Calderόn-Zygmund Operators on Non-homogeneous Metric Measure Spaces

Let(X, d, μ) be a metric measure space satisfying both the upper doubling and the geometrically doubling conditions in the sense of Hyt?nen. In this paper, the authors obtain the boundedness of the commutators of θ-type Calderón-Zygmund operators with RBMO functions from L~∞(μ) into RBMO(μ) and from H_(at)~(1,∞)(μ) into L~1(μ), respectively.As a consequence of these results, they establish the L~p(μ) boundedness of the commutators on the non-homogeneous metric spaces.     

Calderón–Zygmund Type Singular Operators in Weighted Generalized Morrey Spaces

We find conditions for the weighted boundedness of a general class of multidimensional singular integral operators in generalized Morrey spaces \(\mathcal {L}^{p,\varphi }(\mathbb {R}^n,w),\) defined by a function \(\varphi (x,r)\) and radial type weight \(w(|x-x_0|), x_0\in {\mathbb {R}}^{n}.\) These conditions are given in terms of inclusion into \(\mathcal {L}^{p,\varphi }(\mathbb {R}^n,w),\) of a certain integral constructions defined by \(\varphi \) and w. In the case of \(\varphi =\varphi (r)\) we also provide easy to check sufficient conditions for that in terms of indices of \(\varphi \) and w.     

A Weighted Weak Type Endpoint Estimate for the Multilinear Calderón-Zygmund Operators and Its Applications

A weighted weak type endpoint estimate is established for the m-linear operator with Calderón-Zygmund kernel,which was introduced by Coifman and Meyer.As applications,the mapping properties on weighted L~(P1)(R~n)×…×L~(Pm)(R~n)with weight MBω for certain maximal operator MB and general weight ω,and a two-weight weighted norm estimate for this operator,are obtained.