Optimal Embeddings of Bessel-Potential-Type Spaces into Generalized Hölder Spaces Involving k-Modulus of Smoothness

0335002 - MÚ 2010 RIV NL eng J - Článek v odborném periodiku
Gogatishvili, Amiran - Neves, J. S. - Opic, Bohumír
Optimal Embeddings of Bessel-Potential-Type Spaces into Generalized Hölder Spaces Involving k-Modulus of Smoothness.
Potential Analysis. Roč. 32, č. 3 (2010), s. 201-228. ISSN 0926-2601. E-ISSN 1572-929X
Grant CEP: GA ČR GA201/05/2033; GA ČR GA201/08/0383
Výzkumný záměr: CEZ:AV0Z10190503
Klíčová slova: slowly varying functions * Lorentz-Karamata spaces * Rearrangement-invariant Banach function spaces * Bessel potentials * (fractional) Sobolev-type spaces * Hölder-type spaces * Zygmund-type spaces
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 0.853, rok: 2010
http://link.springer.com/article/10.1007%2Fs11118-009-9148-2

We establish necessary and sufficient conditions for embeddings of Bessel potential spaces Hσ X(IRn) with order of smoothness σ (0, n), modelled upon rearrangement invariant Banach function spaces X(IRn), into generalized Hölder spaces (involving k-modulus of smoothness). We apply our results to the case when X(IRn) is the Lorentz-Karamata space Lp,q;b (IRn). In particular, we are able to characterize optimal embeddings of Bessel potential spaces Hσ Lp,q;b (IRn) into generalized Hölder spaces. Applications cover both superlimiting and limiting cases. We also show that our results yield new and sharp embeddings of Sobolev-Orlicz spaces Wk+1Ln/k(log L)α(IRn) and WkLn/k(log L)α(IRn) into generalized Hölder spaces.
Trvalý link: http://hdl.handle.net/11104/0179596