Displaying similar documents to “On definitions of superharmonic functions”

Bounds of Riesz Transforms on L p Spaces for Second Order Elliptic Operators

Zhongwei Shen (2005)

Annales de l’institut Fourier

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Let = -div ( A ( x ) ) be a second order elliptic operator with real, symmetric, bounded measurable coefficients on n or on a bounded Lipschitz domain subject to Dirichlet boundary condition. For any fixed p > 2 , a necessary and sufficient condition is obtained for the boundedness of the Riesz transform ( ) - 1 / 2 on the L p space. As an application, for 1 < p < 3 + ϵ , we establish the L p boundedness of Riesz transforms on Lipschitz domains for operators with V M O coefficients. The range of p is sharp. The closely related boundedness...

Riesz spaces of order bounded disjointness preserving operators

Fethi Ben Amor (2007)

Commentationes Mathematicae Universitatis Carolinae

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Let L , M be Archimedean Riesz spaces and b ( L , M ) be the ordered vector space of all order bounded operators from L into M . We define a Lamperti Riesz subspace of b ( L , M ) to be an ordered vector subspace of b ( L , M ) such that the elements of preserve disjointness and any pair of operators in has a supremum in b ( L , M ) that belongs to . It turns out that the lattice operations in any Lamperti Riesz subspace of b ( L , M ) are given pointwise, which leads to a generalization of the classic Radon-Nikod’ym theorem...

Remark on the inequality of F. Riesz

W. Łenski (2005)

Banach Center Publications

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We prove F. Riesz’ inequality assuming the boundedness of the norm of the first arithmetic mean of the functions | φ | p with p ≥ 2 instead of boundedness of the functions φₙ of an orthonormal system.

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 < α < 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.

Riesz transforms for the Dunkl Ornstein-Uhlenbeck operator

Adam Nowak, Luz Roncal, Krzysztof Stempak (2010)

Colloquium Mathematicae

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We propose a definition of Riesz transforms associated to the Ornstein-Uhlenbeck operator based on the Dunkl Laplacian. In the case related to the group ℤ ₂ it is proved that the Riesz transform is bounded on the corresponding L p spaces, 1 < p < ∞.

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.

Riesz potentials and amalgams

Michael Cowling, Stefano Meda, Roberta Pasquale (1999)

Annales de l'institut Fourier

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Let ( M , d ) be a metric space, equipped with a Borel measure μ satisfying suitable compatibility conditions. An amalgam A p q ( M ) is a space which looks locally like L p ( M ) but globally like L q ( M ) . We consider the case where the measure μ ( B ( x , ρ ) of the ball B ( x , ρ ) with centre x and radius ρ behaves like a polynomial in ρ , and consider the mapping properties between amalgams of kernel operators where the kernel ker K ( x , y ) behaves like d ( x , y ) - a when d ( x , y ) 1 and like d ( x , y ) - b when d ( x , y ) 1 . As an application, we describe Hardy–Littlewood–Sobolev type regularity...