Displaying similar documents to “Global orthogonality implies local almost-orthogonality.”

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].

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...

Pointwise multipliers for reverse Holder spaces

Stephen Buckley (1994)

Studia Mathematica

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We classify weights which map reverse Hölder weight spaces to other reverse Hölder weight spaces under pointwise multiplication. We also give some fairly general examples of weights satisfying weak reverse Hölder conditions.