Displaying similar documents to “Note on a theorem by Reshetnyak-Gurov”

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...

Unrectifiable 1-sets have vanishing analytic capacity.

Guy David (1998)

Revista Matemática Iberoamericana

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We complete the proof of a conjecture of Vitushkin that says that if E is a compact set in the complex plane with finite 1-dimensional Hausdorff measure, then E has vanishing analytic capacity (i.e., all bounded anlytic functions on the complement of E are constant) if and only if E is purely unrectifiable (i.e., the intersection of E with any curve of finite length has zero 1-dimensional Hausdorff measure). As in a previous paper with P. Mattila, the proof relies on a rectifiability...

Removable sets for Lipschitz harmonic functions in the plane.

Guy David, Pertti Mattila (2000)

Revista Matemática Iberoamericana

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The main motivation for this work comes from the century-old Painlevé problem: try to characterize geometrically removable sets for bounded analytic functions in C.

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].