Espaces du type Sobolev sur un espace de Hilbert complexe
We consider generalized square function norms of holomorphic functions with values in a Banach space. One of the main results is a characterization of embeddings of the form , in terms of the type p and cotype q of the Banach space X. As an application we prove -estimates for vector-valued Littlewood-Paley-Stein g-functions and derive an embedding result for real and complex interpolation spaces under type and cotype conditions.
We investigate the Fourier transforms of functions in the Sobolev spaces . It is proved that for any function the Fourier transform f̂ belongs to the Lorentz space , where . Furthermore, we derive from this result that for any mixed derivative the weighted norm can be estimated by the sum of -norms of all pure derivatives of the same order. This gives an answer to a question posed by A. Pełczyński and M. Wojciechowski.
In this work we study the problem in , in , on , in , is a bounded regular domain such that , , , , and are positive functions such...