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We provide some new estimates on Traces in new mixed norm Hardy and Herz type spaces and related new results on Bergman type integral operators in Hardy type spaces and Herz type spaces in the unit ball, in tubular domains over symmetric cones and in bounded strictly pseudoconvex domains with smooth boundary. We in particular generalize in various directions a well-known one dimensional result concerning Traces of Hardy spaces obtained previously in the unit disk and polydisk by various authors. 2010 Mathematics Subject Classification: 30C45.

ON BERGMAN TYPE OPERATORS IN NEW HARDY AND HERZ TYPE ANALYTIC SPACES IN BOUNDED STRICTLY PSEUDOCONVEX AND TUBULAR DOMAINS