×

Extended Cesàro operators between generalized Besov spaces and Bloch type spaces in the unit ball. (English) Zbl 1221.47065

Summary: Let \(g\) be a holomorphic function on the unit ball \(B\) in the \(n\)-dimensional complex space, and denote by \(T_g\) the extended Cesàro operator with symbol \(g\). Let \(0 < p < +\infty\), \(-n - 1 < q < +\infty\), \(q > - 1\) and \(\alpha > 0\). Starting with a brief introduction to well-known results about Cesàro operators, we investigate the boundedness and compactness of \(T_g\) between generalized Besov space \(B(p,q\)) and \(\alpha\)-Bloch space \(\mathcal B^\alpha \) in the unit ball, and also present some necessary and sufficient conditions.

MSC:

47B38 Linear operators on function spaces (general)
46E15 Banach spaces of continuous, differentiable or analytic functions
32A37 Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA))
PDFBibTeX XMLCite
Full Text: DOI arXiv