### Waring's problem in quadratic number fields

J. Cohn (1972)

Acta Arithmetica

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J. Cohn (1972)

Acta Arithmetica

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Pablo Galindo, Domingo Garciá, Manuel Maestre, Jorge Mujica (1994)

Studia Mathematica

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Grzegorz Łysik (1991)

Studia Mathematica

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Krzysztof Bogdan, Tomasz Byczkowski (1999)

Studia Mathematica

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The purpose of the paper is to extend results of the potential theory of the classical Schrödinger operator to the α-stable case. To obtain this we analyze a weak version of the Schrödinger operator based on the fractional Laplacian and we prove the Conditional Gauge Theorem.

Andrew Kepert (1994)

Studia Mathematica

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The existence of a projection onto an ideal I of a commutative group algebra ${L}^{1}\left(G\right)$ depends on its hull Z(I) ⊆ Ĝ. Existing methods for constructing a projection onto I rely on a decomposition of Z(I) into simpler hulls, which are then reassembled one at a time, resulting in a chain of projections which can be composed to give a projection onto I. These methods are refined and examples are constructed to show that this approach does not work in general. Some answers are also given to previously...

Krzysztof Bogdan (1997)

Studia Mathematica

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We study nonnegative functions which are harmonic on a Lipschitz domain with respect to symmetric stable processes. We prove that if two such functions vanish continuously outside the domain near a part of its boundary, then their ratio is bounded near this part of the boundary.

Sagun Chanillo, David Watson, Richard Wheeden (1993)

Studia Mathematica

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We prove two-weight norm estimates for fractional integrals and fractional maximal functions associated with starlike sets in Euclidean space. This is seen to include general positive homogeneous fractional integrals and fractional integrals on product spaces. We consider both weak type and strong type results, and we show that the conditions imposed on the weight functions are fairly sharp.