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Chapter 39 Spaces of analytic functions with integral norm

DOI: 10.1016/s1874-5849(03)80046-3


Abstract We discuss properties of Banach spaces of analytic functions with integral type norms, in particular Hardy spaces and Bergman spaces. We present results about the isomorphic structure of those spaces, subspaces and complemented subspaces, special operators like multipliers and composition operators. The basic results about the real variable theory of H1 spaces are discussed and the connections with complex theory are explained. Isometric questions are also presented.

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