Carleson Measures and Toeplitz operators for weighted Bergman spaces on the unit ball

Abstract: Some new characterizations on Carleson measures for weighted Bergman spaces on the unit ball involving product of functions are obtained. For these we characterize bounded and compact Toeplitz operators between weighted Bergman spaces. The above results are applied to characterize bounded and compact extended Ces`aro operators and pointwise multiplication operators. The results are new even in the case of the unit disk.