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Hardy Spaces (hardy + space)

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Mathematics and Statistics100%

Selected Abstracts

A transmission problem with imperfect contact for an unbounded multiply connected domain

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 4 2010
L. P. Castro
Abstract An analysis of the flux of certain unbounded doubly periodic multiply connected domains with circle disjoint components is performed. This is done under generalized non-ideal contact conditions on the boundary between domain components, which include analytic given data. A formula for the flux that depends on the conductivity of components, their radii, centers, the conductivity of the matrix, and also certain values of special Eisenstein functions is derived. Existence and uniqueness of solution to the problem are obtained by using a transmission problem with imperfect contact for analytic functions in corresponding Hardy spaces. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Parametrized Littlewood,Paley operators on Hardy and weak Hardy spaces

MATHEMATISCHE NACHRICHTEN, Issue 4 2007
Yong Ding
Abstract In this paper, we give the boundedness of the parametrized Littlewood,Paley function on the Hardy spaces and weak Hardy spaces. As the corollaries of the above results, we prove that is of weak type (1, 1) and of type (p, p) for 1 < p < 2, respectively. This results are substantial improvement and extension of some known results. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Estimates of hyperbolic equations in Hardy spaces

MATHEMATISCHE NACHRICHTEN, Issue 1 2003
Chen Chang
Abstract The aim of this paper is to study estimates of hyperbolic equations in Hardy classes. Consider the Cauchy problem P(Dt,Dx)u(t, x) = 0 for x , ,d and t > 0 with the initial conditions Djtu(0, x) = gj (x), j = 0, 1, ,, m , 1. We assume that the symbol ,,(,, ,) of P(Dt,Dx) can be factorized as ,,(,, ,) = (,,,j(,)) where ,j (,) = , j = 1, ,, m. We assume further that gj , Hpk (,d) for j = 1, ,, m , 1. Then the solution u of the problem (3.13) is in Hp(,d) provided k , (d, 1) and < p < ,. Here n = max{n1, ,, nm}. In particular, P(Dt, Dx)u = , ,u = 0 with u(0, x) = f(x) and (0, x) = g(x), then the solution u of the wave equation is in Hp(,d) provided k , (d , 1) and 0 < p < ,. [source]