Abstract
Let g be an analytic function on the unit disc and consider the integration operator of the form \({T_g f(z) = \int_0^z fg'\,d\zeta}\). We derive estimates for the essential and weak essential norms of T g on the spaces H p and BMOA. In particular, on H 1 and BMOA the operator T g is weakly compact if and only if it is compact.
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S. Miihkinen was supported by the Academy of Finland, project 134757.
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Laitila, J., Miihkinen, S. & Nieminen, P.J. Essential norms and weak compactness of integration operators. Arch. Math. 97, 39–48 (2011). https://doi.org/10.1007/s00013-011-0272-z
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DOI: https://doi.org/10.1007/s00013-011-0272-z