On Embeddings for Classes of Functions with Generalized Smoothness on Metric Spaces
- 19 Downloads
Given a metric space with a Borel measure, we consider the classes of functions whose increment is controlled by the measure of a ball containing the corresponding points and a nonnegative function summable with some power. We prove embedding theorems for these spaces defined by two different measures satisfying the doubling condition.
Unable to display preview. Download preview PDF.
- 1.Romanov A. S., “Embedding theorems for a certain function class of Sobolev type on metric spaces,” Sibirsk. Mat. Zh., 45, No. 2, 452–465 (2004).Google Scholar
- 2.Hajlasz P., “Sobolev spaces on an arbitrary metric space,” Potential Anal., 5, No. 4, 403–415 (1996).Google Scholar
- 3.Hajlasz P. and Koskela P., “Sobolev met Poincare,” Mem. Amer. Math. Soc., 688, 1–101 (2000).Google Scholar
- 4.Strömberg J.-O. and Torchinsky A., Weighted Hardy Spaces, Springer-Verlag, Berlin etc. (1989). (Lecture Notes in Mathematics; 1381.)Google Scholar
- 5.Stein E. M., Singular Integrals and Differentiability Properties of Functions [Russian translation], Mir, Moscow (1973). 729Google Scholar