Restrictions of Sobolev W_p^1(R^2)-spaces to planar rectifiable curves

Unions of Rectifiable Curves and the Dimension of Banach Spaces

To any metric space it is possible to associate the cardinal invariant corresponding to the least number of rectifiable curves in the space whose union is not meagre. It is shown that this invariant can vary with the metric space considered, even when restricted to the class of convex subspaces of separable Banach spaces. As a corollary it is obtained that it is consistent with set theory that ...

Sobolev Spaces with Respect to Measures in Curves and Zeros of Sobolev Orthogonal Polynomials

In this paper we obtain some practical criteria to bound the multiplication operator in Sobolev spaces with respect to measures in curves. As a consequence of these results, we characterize the weighted Sobolev spaces with bounded multiplication operator, for a large class of weights. To have bounded multiplication operator has important consequences in Approximation Theory: it implies the unif...

Approximation Theory for Weighted Sobolev Spaces on Curves

In this paper we present a definition of weighted Sobolev spaces on curves and find general conditions under which the spaces are complete. We also prove the density of the polynomials in these spaces for non-closed compact curves and, finally, we find conditions under which the multiplication operator is bounded on the completion of polynomials. These results have applications to the study of ...

Sobolev Spaces

A note on the remainders of rectifiable spaces

In this paper‎, ‎we mainly investigate how the generalized metrizability properties of the remainders affect the metrizability of rectifiable spaces‎, ‎and how the character of the remainders affects the character‎ ‎and the size of a rectifiable space‎. ‎Some results in [A. V‎. ‎Arhangel'skii and J‎. ‎Van Mill‎, ‎On topological groups with a first-countable remainder‎, ‎Topology Proc. 42 (2013...