Displaying similar documents to “Singular integrals on C p α ”

On multilinear singular integrals of Calderón-Zygmund type.

Loukas Grafakos, Rodolfo H. Torres (2002)

Publicacions Matemàtiques

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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....

The work of José Luis Rubio de Francia (III).

Javier Duoandikoetxea (1991)

Publicacions Matemàtiques

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The aim of this paper is to review a set of articles ([6], [10], [11], [13], [16], [25]) of which José Luis Rubio de Francia was author and co-author written between 1985 and 1987.

Regularity properties of singular integral operators

Abdellah Youssfi (1996)

Studia Mathematica

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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...

Estimates for maximal singular integrals

Loukas Grafakos (2003)

Colloquium Mathematicae

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It is shown that maximal truncations of nonconvolution L²-bounded singular integral operators with kernels satisfying Hörmander’s condition are weak type (1,1) and L p -bounded for 1 < p< ∞. Under stronger smoothness conditions, such estimates can be obtained using a generalization of Cotlar’s inequality. This inequality is not applicable here and the point of this article is to treat the boundedness of such maximal singular integral operators in an alternative way.

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

Steve Hofmann (1994)

Revista Matemática Iberoamericana

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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...

Multiple singular integrals and maximal functions along hypersurfaces

Javier Duoandikoetxea (1986)

Annales de l'institut Fourier

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Maximal functions written as convolution with a multiparametric family of positive measures, and singular integrals whose kernel is decomposed as a multiple series of measures, are shown to be bounded in L p , 1 &lt; p &lt; ∞ . The proofs are based on the decomposition of the operators according to the size of the Fourier transform of the measures, assuming some regularity at zero and decay at infinity of these Fourier transforms. Applications are given to homogeneous singular integrals in product spaces...

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

Michel Frazier, Rodolfo Torres, Guido Weiss (1988)

Revista Matemática Iberoamericana

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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) = límε→0 ∫|x-y|&gt;ε K(x-y) f(y) dy = p.v.K * f(x), where f belongs to some class of test functions.

L boundedness of a singular integral operator.

Dashan Fan, Yibiao Pan (1997)

Publicacions Matemàtiques

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In this paper we study a singular integral operator T with rough kernel. This operator has singularity along sets of the form {x = Q(|y|)y'}, where Q(t) is a polynomial satisfying Q(0) = 0. We prove that T is a bounded operator in the space L2(Rn), n ≥ 2, and this bound is independent of the coefficients of Q(t). We also obtain certain Hardy type inequalities related to this operator.