On the Calderon-Zygmund property of Riesz-transform type operators arising in nonlocal equations

Wavelet Decomposition of Calderon - Zygmund Operators on Function Spaces

We make use of the Beylkin-Coifman-Rokhlin wavelet decomposition algorithm on the CalderonZygmund kernel to obtain some fine estimates on the operator and prove the T(\) theorem on Besov and Triebel-Lizorkin spaces. This extends previous results of Frazier et at., and Han and Hofmann. 2000 Mathematics subject classification: primary 42B20, 46B30.

A Simple Proof of the Sharp Weighted Estimate for Calderon-zygmund Operators on Homogeneous Spaces

Here we show that Lerner’s method of local mean oscillation gives a simple proof of theA2 conjecture for spaces of homogeneous type: that is, the linear dependence on the A2 norm for weighted L 2 Calderon-Zygmund operator estimates. In the Euclidean case, the result is due to Hytönen, and for geometrically doubling spaces, Nazarov, Rezinikov, and Volberg obtained the linear bound.

Volterra-Type Operators on Zygmund Spaces

A Calderon - Zygmund extension theorem for abstract

It is shown that if the Boyd indices of the rearrangement invariant Banach function space Lρ(R) are strictly between 0 and 1, ρ is an absolutely continuous function norm, Ω is a domain from R satisfying the restricted cone condition, denoting by ω the restriction of ρ to Ω, there exists an extension operator for the abstract Sobolev space W Lω(Ω). This is a generalization to abstract Sobolev sp...

On the Hyponormal Property of Operators

Let $T$ be a bounded linear operator on a Hilbert space $mathscr{H}$. We say that $T$ has the hyponormal property if there exists a function $f$, continuous on an appropriate set so that $f(|T|)geq f(|T^ast|)$. We investigate the properties of such operators considering certain classes of functions on which our definition is constructed. For such a function $f$ we introduce the $f$-Aluthge tran...