For a smoothly bounded convex domainΩbelong to C^(n)of finite type,let A^(p)(Ω)be the Bergman space onΩwith its reproducing kernel K(·,·).We geometrically characterize such a nonnegative Borel measureμth...For a smoothly bounded convex domainΩbelong to C^(n)of finite type,let A^(p)(Ω)be the Bergman space onΩwith its reproducing kernel K(·,·).We geometrically characterize such a nonnegative Borel measureμthat the Toeplitz operator T_(μ)f(z)=∫_(Ω)f(w)K(z,w)dμ(w)is:(i)bounded from A^(p)(Ω)to A^(q)(Ω),(ii)compact from A^(p)(Ω)to A^(q)(Ω),and(iii)in the Schatten class on A^(2)(Ω).Meanwhile,we can geometrically characterize the boundedness-compactness-Schatten class of the Carleson embedding I_(μ):A^(p)(Ω)→L^(q)(Ω,dμ).展开更多
基金supported by Natural Sciences and Engineering Research Council of Canada(Grant No.#202979)supported by Guangdong Basic and Applied Basic Research Foundation(Grant No.2023A1515110597)。
文摘For a smoothly bounded convex domainΩbelong to C^(n)of finite type,let A^(p)(Ω)be the Bergman space onΩwith its reproducing kernel K(·,·).We geometrically characterize such a nonnegative Borel measureμthat the Toeplitz operator T_(μ)f(z)=∫_(Ω)f(w)K(z,w)dμ(w)is:(i)bounded from A^(p)(Ω)to A^(q)(Ω),(ii)compact from A^(p)(Ω)to A^(q)(Ω),and(iii)in the Schatten class on A^(2)(Ω).Meanwhile,we can geometrically characterize the boundedness-compactness-Schatten class of the Carleson embedding I_(μ):A^(p)(Ω)→L^(q)(Ω,dμ).
