Displaying similar documents to “The traveling salesman problem and harmonic analysis.”

Harmonic analysis and the geometry of subsets of R.

Guy David, Stephen Semmes (1991)

Publicacions Matemàtiques

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This subject has several natural points of view, but we shall start with the one that corresponds to the following question: Is there something like Littlewood-Paley theory which is useful for analyzing the geometry of subsets of R, in much the same way that traditional Littlewood-Paley theory is good for analyzing functions and operators?

Comparisons of kernel functions boundary Harnack principle and relative Fatou theorem on Lipschitz domains

Jang-Mei G. Wu (1978)

Annales de l'institut Fourier

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On a Lipschitz domain D in R n , three theorems on harmonic functions are proved. The first (boundary Harnack principle) compares two positive harmonic functions at interior points near an open subset of the boundary where both functions vanish. The second extends some familiar geometric facts about the Poisson kernel on a sphere to the Poisson kernel on D . The third theorem, on non-tangential limits of quotient of two positive harmonic functions in D , generalizes Doob’s relative Fatou...

A note on the Rellich formula in Lipschitz domains.

Alano Ancona (1998)

Publicacions Matemàtiques

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Let L be a symmetric second order uniformly elliptic operator in divergence form acting in a bounded Lipschitz domain ­Ω of R and having Lipschitz coefficients in Ω­. It is shown that the Rellich formula with respect to Ω­ and L extends to all functions in the domain D = {u ∈ H (Ω­); L(u) ∈ L(­Ω)} of L. This answers a question of A. Chaïra and G. Lebeau.

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...