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- W2079392085 abstract "First, we establish necessary and sufficient conditions for embeddings of Bessel potential spaces $${H^{sigma}X(mathbb R^n)}$$ with order of smoothness less than one, modelled upon rearrangement invariant Banach function spaces $${X(mathbb R^n)}$$ , into generalized Hölder spaces. To this end, we derive a sharp estimate of modulus of smoothness of the convolution of a function $${fin X(mathbb R^n)}$$ with the Bessel potential kernel g σ , 0 < σ < 1. Such an estimate states that if $${g_{sigma}}$$ belongs to the associate space of X, then $$omega(f*g_{sigma},t)precsim intlimits_0^{t^n}s^{frac{sigma}{n}-1}f^*(s),ds quad {rm for,all} quad tin(0,1) quad {rm and,every}quad fin X(mathbb R^n).$$ Second, we characterize compact subsets of generalized Hölder spaces and then we derive necessary and sufficient conditions for compact embeddings of Bessel potential spaces $${H^{sigma}X(mathbb R^n)}$$ into generalized Hölder spaces. We apply our results to the case when $${X(mathbb R^n)}$$ is the Lorentz–Karamata space $${L_{p,q;b}(mathbb R^n)}$$ . In particular, we are able to characterize optimal embeddings of Bessel potential spaces $${H^{sigma}L_{p,q;b}(mathbb R^n)}$$ into generalized Hölder spaces and also compact embeddings of spaces in question. Applications cover both superlimiting and limiting cases." @default.
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- W2079392085 date "2008-07-15" @default.
- W2079392085 modified "2023-09-26" @default.
- W2079392085 title "Optimal embeddings and compact embeddings of Bessel-potential-type spaces" @default.
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- W2079392085 doi "https://doi.org/10.1007/s00209-008-0395-5" @default.
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