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

Weak type estimates for operators of potential type

Richard Wheeden, Shiying Zhao (1996)

Studia Mathematica

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We derive two-weight weak type estimates for operators of potential type in homogeneous spaces. The conditions imposed on the weights are testing conditions of the kind first studied by E. T. Sawyer [4]. We also give some applications to strong type estimates as well as to operators on half-spaces.

Para-accretive functions, the weak boundedness property and the Tb theorem.

Yongsheng Han, Eric T. Sawyer (1990)

Revista Matemática Iberoamericana

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G. David, J.-L. Journé and S. Semmes have shown that if b and b are para-accretive functions on R, then the Tb theorem holds: A linear operator T with Calderón-Zygmund kernel is bounded on L if and only if Tb ∈ BMO, T*b ∈ BMO and MTM has the weak boundedness property. Conversely they showed that when b = b = b, para-accretivity of b is necessary for Tb Theorem to hold. In this paper we show that para-accretivity of both b and b is necessary for the Tb Theorem to hold in general. In addition,...

The fall of the doubling condition in Calderón-Zygmund theory.

Joan Verdera (2002)

Publicacions Matemàtiques

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The most important results of standard Calderón-Zygmund theory have recently been extended to very general non-homogeneous contexts. In this survey paper we describe these extensions and their striking applications to removability problems for bounded analytic functions. We also discuss some of the techniques that allow us to dispense with the doubling condition in dealing with singular integrals. Special attention is paid to the Cauchy Integral. [Proceedings...

Improved Muckenhoupt-Wheeden inequality and weighted inequalities for potential operators.

Y. Rakotondratsimba (1995)

Publicacions Matemàtiques

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By a variant of the standard good λ inequality, we prove the Muckenhoupt-Wheeden inequality for measures which are not necessarily in the Muckenhoupt class. Moreover we can deal with a general potential operator, and consequently we obtain a suitable approach to the two weight inequality for such an operator when one of the weight functions satisfies a reverse doubling condition.

Norm inequalities for potential-type operators.

Sagun Chanillo, Jan-Olov Strömberg, Richard L. Wheeden (1987)

Revista Matemática Iberoamericana

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The purpose of this paper is to derive norm inequalities for potentials of the form Tf(x) = ∫(Rn) f(y)K(x,y)dy,     x ∈ Rn, when K is a Kernel which satisfies estimates like those that hold for the Green function associated with the degenerate elliptic equations studied in [3] and [4].

Measure-preserving quality within mappings.

Stephen Semmes (2000)

Revista Matemática Iberoamericana

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In [6], Guy David introduced some methods for finding controlled behavior in Lipschitz mappings with substantial images (in terms of measure). Under suitable conditions, David produces subsets on which the given mapping is bilipschitz, with uniform bounds for the bilipschitz constant and the size of the subset. This has applications for boundedness of singular integral operators and uniform rectifiability of sets, as in [6], [7], [11], [13]. Some special cases of David's results, concerning...

On the resolvents of dyadic paraproducts.

María Cristina Pereyra (1994)

Revista Matemática Iberoamericana

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We consider the boundedness of certain singular integral operators that arose in the study of Sobolev spaces on Lipschitz curves, [P1]. The standard theory available (David and Journé's T1 Theorem, for instance; see [D]) does not apply to this case becuase the operators are not necessarily Calderón-Zygmund operators, [Ch]. One of these operators gives an explicit formula for the resolvent at λ = 1 of the dyadic paraproduct, [Ch].