caa a22 4500 467931518 CHVBK 20180406152945.0 cr unu---uuuuu 170328e20060701xx s 000 0 eng 10.1007/s00020-005-1391-3 doi (NATIONALLICENCE)springer-10.1007/s00020-005-1391-3 Carleson Measures for Spaces of Dirichlet Type [Elektronische Daten] [Daniel Girela, José Peláez] Abstract.: If 0 < p < ∞ and α > −1, the space $$\mathcal{D}_\alpha ^p $$ consists of those functions f which are analytic in the unit disc $$\mathbb{D}$$ and have the property that f ′ belongs to the weighted Bergman space Aαp. In 1999, Z. Wu obtained a characterization of the Carleson measures for the spaces $$\mathbb{D}_\alpha ^p$$ for certain values of p and α. In particular, he proved that, for 0<p≤2, the Carleson measures for the space $$\mathbb{D}_{p - 1}^p$$ are precisely the classical Carleson measures. Wu also conjectured that this result remains true for 2<p<∞. In this paper we prove that this conjecture is false. Indeed, we prove that if 2<p<∞, then there exists g analytic in $$\mathbb{D}$$ such that the measureμg,p on $$\mathbb{D}$$ defined by dμg,p (z)=(1 − |z|2)p - 1| g ′ (z)|pdxdy is not a Carleson measure for $$\mathcal{D}_{p - 1}^p$$ but is a classical Carleson measure. We obtain also some sufficient conditions for multipliers of the spaces $$\mathcal{D}_{p - 1}^p .$$ Birkhäuser Verlag, Basel, 2006 Carleson measures nationallicence Bergman spaces nationallicence Dirichlet spaces nationallicence multipliers nationallicence Girela Daniel Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, 29071, Málaga, Spain aut Peláez José Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, 29071, Málaga, Spain aut Integral Equations and Operator Theory Birkhäuser-Verlag; www.birkhauser.ch 55/3(2006-07-01), 415-427 0378-620X 55:3<415 2006 55 20 https://doi.org/10.1007/s00020-005-1391-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00020-005-1391-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Girela Daniel Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, 29071, Málaga, Spain aut NATIONALLICENCE 700 1- Peláez José Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, 29071, Málaga, Spain aut NATIONALLICENCE 773 0- Integral Equations and Operator Theory Birkhäuser-Verlag; www.birkhauser.ch 55/3(2006-07-01), 415-427 0378-620X 55:3<415 2006 55 20 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer