Displaying similar documents to “The boundedness of Calderón-Zygmund operators on the spaces Fpα,q.”

Regularity properties of singular integral operators

Abdellah Youssfi (1996)

Studia Mathematica

Similarity:

For s>0, we consider bounded linear operators from D ( ℝ n ) into D ' ( ℝ n ) whose kernels K satisfy the conditions | ∂ x γ K ( x , y ) | ≤ C γ | x - y | - n + s - | γ | for x≠y, |γ|≤ [s]+1, | ∇ y ∂ x γ K ( x , y ) | ≤ C γ | x - y | - n + s - | γ | - 1 for |γ|=[s], x≠y. We establish a new criterion for the boundedness of these operators from L 2 ( ℝ n ) into the homogeneous Sobolev space Ḣ s ( ℝ n ) . This is an extension of the well-known T(1) Theorem due to David and Journé. Our arguments make use of the function T(1) and the BMO-Sobolev space. We give some applications to the Besov and Triebel-Lizorkin spaces as well as some...

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-type reproducing formula and the Tb theorem.

Yong Sheng Han (1994)

Revista Matemática Iberoamericana

Similarity:

In this paper we use the Calderón-Zygmund operator theory to prove a Calderón type reproducing formula associated with a para-accretive function. Using our Calderón-type reproducing formula we introduce a new class of the Besov and Triebel-Lizorkin spaces and prove a Tb theorem for these new spaces.

On singular integrals of Calderón-type in R and BMO.

Steve Hofmann (1994)

Revista Matemática Iberoamericana

Similarity:

We prove Lp (and weighted Lp) bounds for singular integrals of the form p.v.  ∫Rn E (A(x) - A(y) / |x - y|) (Ω(x - y) / |x - y|n) f(y) dy, where E(t) = cos t if Ω is odd, and E(t) = sin t if Ω is even, and where ∇ A ∈ BMO. Even in the case that Ω is smooth, the theory of singular integrals with rough kernels plays a key role in the...

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 ∞ 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...

Hardy space estimates for multilinear operators (I).

Ronald R. Coifman, Loukas Grafakos (1992)

Revista Matemática Iberoamericana

Similarity:

In this article we study bilinear operators given by inner products of finite vectors of Calderón-Zygmund operators. We find that necessary and sufficient condition for these operators to map products of Hardy spaces into Hardy spaces is to have a certain number of moments vanishing and under this assumption we prove a Hölder-type inequality in the H space context.