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

2011 ◽  
pp. 1-27 ◽  
Author(s):  
Amiran Gogatishvili ◽  
Júlio Neves ◽  
Bohumír Opic
Keyword(s):  
Modulus Of Smoothness ◽  
Bessel Potential ◽  
Hölder Spaces ◽  
Compact Embeddings ◽  
Potential Type ◽  
Type Spaces ◽  
Holder Spaces

scholarly journals Optimal embeddings and compact embeddings of Bessel-potential-type spaces

2008 ◽  
Vol 262 (3) ◽  
pp. 645-682 ◽  
Author(s):  
Amiran Gogatishvili ◽  
Júlio S. Neves ◽  
Bohumír Opic
Keyword(s):  
Bessel Potential ◽  
Compact Embeddings ◽  
Potential Type ◽  
Type Spaces

Riesz Potential With Logarithmic Kernel in Generalized Hölder Spaces

2021 ◽  
pp. 275-296
Author(s):  
Boris Grigorievich Vakulov ◽  
Yuri Evgenievich Drobotov
Keyword(s):  
Financial Analysis ◽  
Riesz Potential ◽  
Inverse Operator ◽  
Mathematical Physics ◽  
Hölder Spaces ◽  
Fractal Sets ◽  
Logarithmic Kernel ◽  
Potential Type ◽  
Holder Spaces ◽  
Potential Type Operators

The multidimensional Riesz potential type operators are of interest within mathematical modelling in economics, mathematical physics, and other, both theoretical and applied, disciplines as they play a significant role for analysis on fractal sets. Approaches of operator theory are relevant to researching various equations, which are widespread in financial analysis. In this chapter, integral equations with potential type operators are considered for functions from generalized Hölder spaces, which provide content terminology for formalizing the concept of smoothness, briefly described in the presented chapter. Results on potentials defined on the unit sphere are described for convenience of the analysis. An inverse operator for the Riesz potential with a logarithmic kernel is carried out, and the isomorphisms between generalized Hölder spaces are proven.

Optimality of embeddings of Bessel-potential-type spaces into Lorentz–Karamata spaces

2004 ◽  
Vol 134 (6) ◽  
pp. 1127-1147 ◽  
Author(s):  
Amiran Gogatishvili ◽  
Bohumír Opic ◽  
Júlio S. Neves
Keyword(s):  
Embedding Theorems ◽  
Bessel Potential ◽  
Potential Type ◽  
Type Spaces ◽  
Growth Envelopes ◽  
Bessel Potential Spaces

We establish sharpness of embedding theorems for Bessel-potential spaces modelled upon Lorentz–Karamata (LK) spaces and we prove the non-compactness of such embeddings. Target spaces in our embeddings are LK spaces. As a consequence of our results, we get growth envelopes of Bessel-potential spaces modelled upon LK spaces.

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