Authors: | Stević, Stevo | Affiliations: | Mathematical Institute of the Serbian Academy of Sciences and Arts | Title: | Extended cesàro operators between mixed-norm spaces and bloch-type spaces in the unit ball | Journal: | Houston Journal of Mathematics | Volume: | 36 | Issue: | 3 | First page: | 843 | Last page: | 858 | Issue Date: | 29-Oct-2010 | Rank: | M22 | ISSN: | 0362-1588 | Abstract: | This paper studies the boundedness and compactness of the following, so called, extended Cesàro operator Tg(fz) = ∫01 f(tz) Rg(tz)dt/t, z ε B. between the mixed-norm space H(p, q, ℓ) and the Bloch-type space Bμ (or the little Bloch-type space Bμ,o) of holomorphic functions on the unit ball B in Cn. For the special (but still very general) case of the weighted Bergman space Aαp the paper calculates the norm of the operator for the case p > 0 and finds some upper and lower bounds for the essential norm of the operator when p > 1. When the reciprocal function of μ is Lebesgue integrable we completely characterize the boundedness and compactness of the operator Tg: Bμ → H (p, q, ℓ). |
Keywords: | Bloch-type space | Boundedness | Compactness | Essential norm | Extended cesà | Mixed-norm space | Ro operators | Unit ball | Publisher: | University of Houston |
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