Abstract
It is shown that the Berezin transform B on L p(D), where D is the unit disc, has norm \(\left\| B \right\|_p = \tfrac{{p + 1}}{{p^2 }}\tfrac{\pi }{{\sin (\pi /p)}}(1 < p \leqslant \infty )\). Furthermore, the norms of a family of operators (on L p(D)) whose kernels are moduli of Bergman type kernels are also calculated.
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Partially supported by MNZZS, Grant \(\mathcal{N}^o \) ON144010
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Dostanić, M. Norm of Berezin transformon L p space. J Anal Math 104, 13–23 (2008). https://doi.org/10.1007/s11854-008-0014-8
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DOI: https://doi.org/10.1007/s11854-008-0014-8