Regularity properties of singular integral operators

Abdellah Youssfi

Displaying similar documents to “Regularity properties of singular integral operators”

The boundedness of Calderón-Zygmund operators on the spaces F .

Michel Frazier, Rodolfo Torres, Guido Weiss (1988)

Revista Matemática Iberoamericana

Similarity:

Calderón-Zygmund operators are generalizations of the singular integral operators introduced by Calderón and Zygmund in the fifties [CZ]. These singular integrals are principal value convolutions of the form Tf(x) = lím_ε→0 ∫_|x-y|>ε K(x-y) f(y) dy = p.v.K * f(x), where f belongs to some class of test functions.

Two problems of Calderón-Zygmund theory on product-spaces

Jean-Lin Journé (1988)

Annales de l'institut Fourier

Similarity:

R. Fefferman has shown that, on a product-space with two factors, an operator T bounded on $L^{2}$ maps $L^{\infty}$ into BMO of the product if the mean oscillation on a rectangle R of the image of a bounded function supported out of a multiple R’ of R, is dominated by $C | R |^{s} | R |^{- s}$ , for some $s > 0$ . We show that this result does not extend in general to the case where E has three or more factors but remains true in this case if in addition T is a convolution operator, provided $s > s_{0} (E)$ . We also show that the Calderon-Coifman...

Singular integrals on $C_{p}^{α}$

Robert Sharpley, Yong-Sun Shim (1989)

Studia Mathematica

Similarity:

Generalizations of Calderón-Zygmund operators

Kôzô Yabuta (1985)

Studia Mathematica

Similarity:

Weighted estimates for commutators of linear operators

Josefina Alvarez, Richard Bagby, Douglas Kurtz, Carlos Pérez (1993)

Studia Mathematica

Similarity:

We study boundedness properties of commutators of general linear operators with real-valued BMO functions on weighted $L^{p}$ spaces. We then derive applications to particular important operators, such as Calderón-Zygmund type operators, pseudo-differential operators, multipliers, rough singular integrals and maximal type operators.

A Hörmander-type spectral multiplier theorem for operators without heat kernel

Sönke Blunck (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

Hörmander’s famous Fourier multiplier theorem ensures the $L_{p}$ -boundedness of $F (- Δ_{ℝ} D)$ whenever $F \in ℋ (s)$ for some $s > \frac{D}{2}$ , where we denote by $ℋ (s)$ the set of functions satisfying the Hörmander condition for $s$ derivatives. Spectral multiplier theorems are extensions of this result to more general operators $A \geq 0$ and yield the $L_{p}$ -boundedness of $F (A)$ provided $F \in ℋ (s)$ for some $s$ sufficiently large. The harmonic oscillator $A = - Δ_{ℝ} + x^{2}$ shows that in general $s > \frac{D}{2}$ is not sufficient even if $A$ has a heat kernel satisfying gaussian estimates. In...

On multilinear singular integrals of Calderón-Zygmund type.

Loukas Grafakos, Rodolfo H. Torres (2002)

Publicacions Matemàtiques

Similarity:

A variety of results regarding multilinear singular Calderón-Zygmund integral operators is systematically presented. Several tools and techniques for the study of such operators are discussed. These include new multilinear endpoint weak type estimates, multilinear interpolation, appropriate discrete decompositions, a multilinear version of Schur's test, and a multilinear version of the T1 Theorem suitable for the study of multilinear pseudodifferential and translation invariant operators....

Calderón-Zygmund operators on product spaces.

Jean-Lin Journé (1985)

Revista Matemática Iberoamericana

Similarity:

The trace inequality and eigenvalue estimates for Schrödinger operators

R. Kerman, Eric T. Sawyer (1986)

Annales de l'institut Fourier

Similarity:

Suppose $Φ$ is a nonnegative, locally integrable, radial function on $R^{n}$ , which is nonincreasing in $| x |$ . Set $(T f) (x) = \int_{R^{n}} Φ (x - y) f (y) d y$ when $f \geq 0$ and $x \in R^{n}$ . Given $1 < p < \infty$ and $v \geq 0$ , we show there exists $C > 0$ so that $\int_{R^{n}} (T f) (x)^{p} v (x) d x \leq C \int_{R^{n}} f (x)^{p} d x$ for all $f \geq 0$ , if and only if $C^{'} > 0$ exists with $\int_{Q} T (x_{Q} v) (x)^{p^{'}} d x \leq C^{'} \int_{Q} v (x) d x < \infty$ for all dyadic cubes Q, where $p^{'} = p / (p - 1)$ . This result is used to refine recent estimates of C.L. Fefferman and D.H. Phong on the distribution of eigenvalues of Schrödinger operators.