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Characterization of traces of the weighted Sobolev space $W^{1, p} (Ω, d_{M}^{ϵ})$ on $M$

Aleš Nekvinda — 1993

Czechoslovak Mathematical Journal

Decomposition of the weighted Sobolev space $W^{1, p} (Ω, d_{M}^{ϵ})$ and its traces

Aleš Nekvinda — 1993

Czechoslovak Mathematical Journal

A Cantor set in the plane that is not σ-monotone

Aleš Nekvinda; Ondřej Zindulka — 2011

Fundamenta Mathematicae

A metric space (X,d) is monotone if there is a linear order < on X and a constant c such that d(x,y) ≤ cd(x,z) for all x < y < z in X, and σ-monotone if it is a countable union of monotone subspaces. A planar set homeomorphic to the Cantor set that is not σ-monotone is constructed and investigated. It follows that there is a metric on a Cantor set that is not σ-monotone. This answers a question raised by the second author.

A difference between continuous and absolutely continuous norms in Banach function spaces

Jan Lang; Aleš Nekvinda — 1997

Czechoslovak Mathematical Journal

On examples we show a difference between a continuous and absolutely continuous norm in Banach function spaces.

Traces of a weighted Sobolev space in a singular case

Jan Lang; Aleš Nekvinda — 1995

Czechoslovak Mathematical Journal

A note on the Dirichlet problem for the elliptic linear operator in Sobolev spaces with weight $d_{M}^{ϵ}$

Aleš Nekvinda; Luboš Pick — 1988

Commentationes Mathematicae Universitatis Carolinae

A simple proof of the Rademacher theorem

Aleš Nekvinda; Luděk Zajíček — 1988

Časopis pro pěstování matematiky

Optimal estimates for the fractional Hardy operator

Yoshihiro Mizuta; Aleš Nekvinda; Tetsu Shimomura — 2015

Studia Mathematica

Let $A_{α} f (x) = {| B (0, | x |) |}^{- α / n} \int_{B (0, | x |)} f (t) d t$ be the n-dimensional fractional Hardy operator, where 0 < α ≤ n. It is well-known that $A_{α}$ is bounded from $L^{p}$ to $L^{p_{α}}$ with $p_{α} = n p / (α p - n p + n)$ when n(1-1/p) < α ≤ n. We improve this result within the framework of Banach function spaces, for instance, weighted Lebesgue spaces and Lorentz spaces. We in fact find a ’source’ space $S_{α, Y}$ , which is strictly larger than X, and a ’target’ space $T_{Y}$ , which is strictly smaller than Y, under the assumption that $A_{α}$ is bounded from X into Y and the Hardy-Littlewood maximal operator...

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Currently displaying 1 – 8 of 8

Characterization of traces of the weighted Sobolev space $W^{1, p} (Ω, d_{M}^{ϵ})$ on $M$

Decomposition of the weighted Sobolev space $W^{1, p} (Ω, d_{M}^{ϵ})$ and its traces

A Cantor set in the plane that is not σ-monotone

A difference between continuous and absolutely continuous norms in Banach function spaces

Traces of a weighted Sobolev space in a singular case

A note on the Dirichlet problem for the elliptic linear operator in Sobolev spaces with weight $d_{M}^{ϵ}$

A simple proof of the Rademacher theorem

Optimal estimates for the fractional Hardy operator