Convolution Calderón-Zygmund singular integral operators with rough kernels

A Note on Calderón-zygmund Singular Integral Convolution Operators

L Bounds for Singular Integrals and Maximal Singular Integrals with Rough Kernels

Convolution type Calderón-Zygmund singular integral operators with rough kernels p.v. Ω(x)/|x| are studied. A condition on Ω implying that the corresponding singular integrals and maximal singular integrals map L → L for 1 < p < ∞ is obtained. This condition is shown to be different from the condition Ω ∈ H1(Sn−1).

Lp BOUNDS FOR SINGULAR INTEGRALS AND MAXIMAL SINGULAR

Convolution type Calderr on-Zygmund singular integral operators with rough kernels p.v. (x)=jxj n are studied. A condition on implying that the corresponding singular integrals and maximal singular integrals map L p ! L p for 1 < p < 1 is obtained. This condition is shown to be diierent from the condition 2 H 1 (S n?1).

Weak Type Estimates and Cotlar Inequalities for Calderón-zygmund Operators on Nonhomogeneous Spaces

The classical theory of Calderón–Zygmund operators started with the study of convolution operators on the real line having singular kernels. (A typical example of such an operator is the so called Hilbert transform, defined by Hf(t) = ∫ R f(s) ds t−s .) Later it has developed into a large branch of analysis covering a quite wide class of singular integral operators on abstract measure spaces (s...

Minimal Regularity Conditions for the End-point Estimate of Bilinear Calderón-zygmund Operators

A crucial property addressed in the linear Calderón-Zygmund theory, going back to the founding article [1], is the fact that operators bounded on L whose kernels possess certain regularity are in fact bounded on every L space for 1 < p < ∞. Moreover, such a regularity assumption implies, together with the L-boundedness of the operator, a weak-type end-point estimate in L. From these continuity ...