For a holomorphic function f on the unit ball B^N of C^N, it is proved that the reduced Hankel oporator R_f on Hardy space H^2(B^N) is of Schatten class S_p for p≥1 if and only if f is in a corresponding Sobolev space.
Let B^n be the unit ball in C^n with dm the normalized Lebesgue measure on it. We de note by H(B^n) the set of holomorphic functions on B^n. Let L_a^2(B^n) be a Bergrnan space, P an orthogonal projection from L^2(B^n,...Let B^n be the unit ball in C^n with dm the normalized Lebesgue measure on it. We de note by H(B^n) the set of holomorphic functions on B^n. Let L_a^2(B^n) be a Bergrnan space, P an orthogonal projection from L^2(B^n, dm) onto L_a^2(B^n). For f∈H(B^n), define the展开更多
Denote the unit open ball of C^N by B=B^N with dm the normalized Lebesgue measure on B^N. Let L_α~2 be a Bergman space consisting of analytic functions in L^2 (B, dm).For f∈ H (B), define the Hankel operator H_f^- a...Denote the unit open ball of C^N by B=B^N with dm the normalized Lebesgue measure on B^N. Let L_α~2 be a Bergman space consisting of analytic functions in L^2 (B, dm).For f∈ H (B), define the Hankel operator H_f^- as follows:展开更多
文摘For a holomorphic function f on the unit ball B^N of C^N, it is proved that the reduced Hankel oporator R_f on Hardy space H^2(B^N) is of Schatten class S_p for p≥1 if and only if f is in a corresponding Sobolev space.
文摘Let B^n be the unit ball in C^n with dm the normalized Lebesgue measure on it. We de note by H(B^n) the set of holomorphic functions on B^n. Let L_a^2(B^n) be a Bergrnan space, P an orthogonal projection from L^2(B^n, dm) onto L_a^2(B^n). For f∈H(B^n), define the
文摘Denote the unit open ball of C^N by B=B^N with dm the normalized Lebesgue measure on B^N. Let L_α~2 be a Bergman space consisting of analytic functions in L^2 (B, dm).For f∈ H (B), define the Hankel operator H_f^- as follows:
