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Carleson measures, multipliers and integration operators for spaces of Dirichlet type |
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| Authors: | Daniel Girela,José Á ngel Pelá ez |
| Affiliation: | a Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, Campus de Teatinos, 29071 Málaga, Spain b Departamento de Análisis Matemático, Universidad de Sevilla, Avenida de la Reina Mercedes, Apartado de Correos 1160, 41080 Sevilla, Spain |
| Abstract: | For 0<p<∞ and α>−1, we let  denote the space of those functions f which are analytic in the unit disc  and satisfy  . In this paper we characterize the positive Borel measures μ in D such that  , 0<p<q<∞. We also characterize the pointwise multipliers from  to  (0<p<q<∞) if p−2<α<p. In particular, we prove that if  the only pointwise multiplier from  to  (0<p<q<∞) is the trivial one. This is not longer true for  and we give a number of explicit examples of functions which are multipliers from  to  for this range of values. |
| Keywords: | Spaces of Dirichlet type Bergman spaces Carleson measures Multipliers Integration operators Inner functions |
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