Displaying similar documents to “On the A -integrability of singular integral transforms”

Harmonic spaces associated with adjoints of linear elliptic operators

Peter Sjögren (1975)

Annales de l'institut Fourier

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Let L be an elliptic linear operator in a domain in R n . We imposse only weak regularity conditions on the coefficients. Then the adjoint L * exists in the sense of distributions, and we start by deducing a regularity theorem for distribution solutions of equations of type L * u = given distribution. We then apply to L * R.M. Hervé’s theory of adjoint harmonic spaces. Some other properties of L * are also studied. The results generalize earlier work of the author.

Boundary behaviour of harmonic functions in a half-space and brownian motion

D. L. Burkholder, Richard F. Gundy (1973)

Annales de l'institut Fourier

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Let u be harmonic in the half-space R + n + 1 , n 2 . We show that u can have a fine limit at almost every point of the unit cubs in R n = R + n + 1 but fail to have a nontangential limit at any point of the cube. The method is probabilistic and utilizes the equivalence between conditional Brownian motion limits and fine limits at the boundary. In R + 2 it is known that the Hardy classes H p , 0 < p < , may be described in terms of the integrability of the nontangential maximal function, or, alternatively, in terms...

Duality on vector-valued weighted harmonic Bergman spaces

Salvador Pérez-Esteva (1996)

Studia Mathematica

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We study the duals of the spaces A p α ( X ) of harmonic functions in the unit ball of n with values in a Banach space X, belonging to the Bochner L p space with weight ( 1 - | x | ) α , denoted by L p α ( X ) . For 0 < α < p-1 we construct continuous projections onto A p α ( X ) providing a decomposition L p α ( X ) = A p α ( X ) + M p α ( X ) . We discuss the conditions on p, α and X for which A p α ( X ) * = A q α ( X * ) and M p α ( X ) * = M q α ( X * ) , 1/p+1/q = 1. The last equality is equivalent to the Radon-Nikodým property of X*.

An inversion formula and a note on the Riesz kernel

Andrejs Dunkels (1976)

Annales de l'institut Fourier

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For potentials U K T = K * T , where K and T are certain Schwartz distributions, an inversion formula for T is derived. Convolutions and Fourier transforms of distributions in ( D L ' p ) -spaces are used. It is shown that the equilibrium distribution with respect to the Riesz kernel of order α , 0 &lt; α &lt; m , of a compact subset E of R m has the following property: its restriction to the interior of E is an absolutely continuous measure with analytic density which is expressed by an explicit formula.

On the boundary limits of harmonic functions with gradient in L p

Yoshihiro Mizuta (1984)

Annales de l'institut Fourier

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This paper deals with tangential boundary behaviors of harmonic functions with gradient in Lebesgue classes. Our aim is to extend a recent result of Cruzeiro (C.R.A.S., Paris, 294 (1982), 71–74), concerning tangential boundary limits of harmonic functions with gradient in L n ( R + n ) , R + n denoting the upper half space of the n -dimensional euclidean space R n . Our method used here is different from that of Nagel, Rudin and Shapiro (Ann. of Math., 116 (1982), 331–360); in fact, we use the integral representation...

On separately subharmonic functions (Lelong’s problem)

A. Sadullaev (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

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The main result of the present paper is : every separately-subharmonic function u ( x , y ) , which is harmonic in y , can be represented locally as a sum two functions, u = u * + U , where U is subharmonic and u * is harmonic in y , subharmonic in x and harmonic in ( x , y ) outside of some nowhere dense set S .

Mapping properties of fundamental operators in harmonic analysis related to Bessel operators

Jorge J. Betancor, Eleonor Harboure, Adam Nowak, Beatriz Viviani (2010)

Studia Mathematica

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We obtain sharp power-weighted L p , weak type and restricted weak type inequalities for the heat and Poisson integral maximal operators, Riesz transform and a Littlewood-Paley type square function, emerging naturally in the harmonic analysis related to Bessel operators.