Displaying similar documents to “Vector-valued Calderón-Zygmund theory and Carleson measures on spaces of homogeneous nature”

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

José Luis Torrea (1991)

Publicacions Matemàtiques

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The aim of these pages is to give the reader an idea about the first part of the mathematical life of José Luis Rubio de Francia.

Weighted inequalities and vector-valued Calderón-Zygmund operators on non-homogeneous spaces.

José García Cuerva, José María Martell (2000)

Publicacions Matemàtiques

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Recently, F. Nazarov, S. Treil and A. Volberg (and independently X. Tolsa) have extended the classical theory of Calderón-Zygmund operators to the context of a non-homogeneous space (X,d,μ) where, in particular, the measure μ may be non-doubling. In the present work we study weighted inequalities for these operators. Specifically, for 1 < p < ∞, we identify sufficient conditions for the weight on one side, which guarantee the existence of another weight in the other side,...

Vector valued inequalities for strongly singular Calderón-Zygmund operators.

Josefina Alvarez, Mario Milman (1986)

Revista Matemática Iberoamericana

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In this article we consider a theory of vector valued strongly singular operators. Our results include Lp, Hp and BMO continuity results. Moreover, as is well known, vector valued estimates are closely related to weighted norm inequalities. These results are developed in the first four sections of our paper. In section 5 we use our vector valued singular integrals to estimate the corresponding maximal operators. Finally in section 6 we discuss...

Vector-valued inequalities with weights.

Luz M. Fernández-Cabrera, José L. Torrea (1993)

Publicacions Matemàtiques

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This paper deals with the following problem: Let T be a given operator. Find conditions on v(x) (resp. u(x)) such that ∫ |Tf(x)|pu(x) dx ≤ C ∫ |f(x)|pv(x) dx is satisfied for some u(x) (resp. v(x)). Using vector-valued inequalities the problem is solved for: Carleson's maximal operator of Fourier partial sums, Littlewood-Paley square functions, Hilbert transform of functions...

A proof of the weak (1,1) inequality for singular integrals with non doubling measures based on a Calderón-Zygmund decomposition.

Xavier Tolsa (2001)

Publicacions Matemàtiques

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Given a doubling measure μ on R, it is a classical result of harmonic analysis that Calderón-Zygmund operators which are bounded in L(μ) are also of weak type (1,1). Recently it has been shown that the same result holds if one substitutes the doubling condition on μ by a mild growth condition on μ. In this paper another proof of this result is given. The proof is very close in spirit to the classical argument for doubling measures and it is based on a new Calderón-Zygmund decomposition...