A Compact Embedding for Sequence Spaces

Embedding Orlicz Sequence Spaces into C(α)

Let M be a non-degenerate Orlicz function such that there exist ǫ > 0 and 0 < s < 1 with ∑ ∞ i=1 M(ǫs)/M(s) < ∞. It is shown that the Orlicz sequence space hM is isomorphic to a subspace of C(ω). It is also shown that for any non-degenerate Orlicz function M , hM does not embed into C(α) for any α < ω .

Embedding measure spaces

‎For a given measure space $(X,{mathscr B},mu)$ we construct all measure spaces $(Y,{mathscr C},lambda)$ in which $(X,{mathscr B},mu)$ is embeddable‎. ‎The construction is modeled on the ultrafilter construction of the Stone--v{C}ech compactification of a completely regular topological space‎. ‎Under certain conditions the construction simplifies‎. ‎Examples are given when this simplification o...

On the characterization of the compact embedding of Sobolev spaces

For every positive regular Borel measure, possibly infinite valued, vanishing on all sets of p-capacity zero, we characterize the compactness of the embedding W (R ) ∩ L(R , μ) ↪→ L(R ) in terms of the qualitative behavior of some characteristic PDE. This question is related to the well posedness of a class of geometric inequalities involving the torsional rigidity and the spectrum of the Diric...

A New Class of Banach Sequence Spaces

embedding measure spaces

‎for a given measure space $(x,{mathscr b},mu)$ we construct all measure spaces $(y,{mathscr c},lambda)$ in which $(x,{mathscr b},mu)$ is embeddable‎. ‎the construction is modeled on the ultrafilter construction of the stone--v{c}ech compactification of a completely regular topological space‎. ‎under certain conditions the construction simplifies‎. ‎examples are given when this simplification o...