We completely characterize the boundedness of area operators from the Bergman spaces A_(α)^(p)(Bn)to the Lebesgue spaces L^(q)(S_(n))for all 0<p,q<∞.For the case n=1,some partial results were previously obtain...We completely characterize the boundedness of area operators from the Bergman spaces A_(α)^(p)(Bn)to the Lebesgue spaces L^(q)(S_(n))for all 0<p,q<∞.For the case n=1,some partial results were previously obtained by Wu in[Wu,Z.:Volterra operator,area integral and Carleson measures,Sci.China Math.,54,2487–2500(2011)].Especially,in the case q<p and q<s,we obtain some characterizations for the area operators to be bounded.We solve the cases left open there and extend the results to n-complex dimension.展开更多
We completely describe the boundedness and compactness of Hankel operators with general symbols acting on Bergman spaces with exponential type weights.
基金partially supported by NSFC(Grant Nos.12171150,11771139)partially supported by NSFC(Grant Nos.12171373,12371136)+2 种基金ZJNSF(Grant No.LY20A010008)supported by the grants MTM2017-83499-P(Ministerio de Educación y Ciencia)2017SGR358(Generalitat de Catalunya)。
文摘We completely characterize the boundedness of area operators from the Bergman spaces A_(α)^(p)(Bn)to the Lebesgue spaces L^(q)(S_(n))for all 0<p,q<∞.For the case n=1,some partial results were previously obtained by Wu in[Wu,Z.:Volterra operator,area integral and Carleson measures,Sci.China Math.,54,2487–2500(2011)].Especially,in the case q<p and q<s,we obtain some characterizations for the area operators to be bounded.We solve the cases left open there and extend the results to n-complex dimension.
基金supported by National Natural Science Foundation of China(Grant No.11771139)supported by Ministerio de Educación y Ciencia(Grant No.MTM2017-83499-P)Generalitat de Catalunya(Grant No.2017SGR358)。
文摘We completely describe the boundedness and compactness of Hankel operators with general symbols acting on Bergman spaces with exponential type weights.
