Characterization of traces of the weighted Sobolev space on
Decomposition of the weighted Sobolev space and its traces
A Cantor set in the plane that is not σ-monotone
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
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
A note on the Dirichlet problem for the elliptic linear operator in Sobolev spaces with weight
A simple proof of the Rademacher theorem
Optimal estimates for the fractional Hardy operator
Let be the n-dimensional fractional Hardy operator, where 0 < α ≤ n. It is well-known that is bounded from to with 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 , which is strictly larger than X, and a ’target’ space , which is strictly smaller than Y, under the assumption that is bounded from X into Y and the Hardy-Littlewood maximal operator...
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