Displaying similar documents to “A multivalued fixed point theorem in ultrametric spaces.”

On sharp reiteration theorems and weighted norm inequalities

Jesús Bastero, Mario Milman, Francisco Ruiz (2000)

Studia Mathematica

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We prove sharp end forms of Holmstedt's reiteration theorem which are closely connected with a general form of Gehring's Lemma. Reverse type conditions for the Hardy-Littlewood-Pólya order are considered and the maximal elements are shown to satisfy generalized Gehring conditions. The methods we use are elementary and based on variants of reverse Hardy inequalities for monotone functions.

Rearrangement of series in nonnuclear spaces

Wojciech Banaszczyk (1993)

Studia Mathematica

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It is proved that if a metrizable locally convex space is not nuclear, then it does not satisfy the Lévy-Steinitz theorem on rearrangement of series.

The boundary Harnack principle for the fractional Laplacian

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.

On certain nonstandard Calderón-Zygmund operators

Steve Hofmann (1994)

Studia Mathematica

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We formulate a version of the T1 theorem which enables us to treat singular integrals whose kernels need not satisfy the usual smoothness conditions. We also prove a weighted version. As an application of the general theory, we consider a class of multilinear singular integrals in n related to the first Calderón commutator, but with a kernel which is far less regular.

Isoperimetric problem for uniform enlargement

S. Bobkov (1997)

Studia Mathematica

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We consider an isoperimetric problem for product measures with respect to the uniform enlargement of sets. As an example, we find (asymptotically) extremal sets for the infinite product of the exponential measure.