Spaces of analytic functions in a region with an angle |
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Authors: | A M Shikhvatov |
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Institution: | 1. Far-Eastern State University, USSR
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Abstract: | In this paper we consider the space Ap of analytic functions which are p-power integrable in a region with an angle. We find a set of numbers p and q (1/p+1/q=1) (which depend on the magnitude of the angle) for which the spaces Ap and Aq are mutually conjugate. In each of these spaces we introduce the orthonormal system $$e_n = \sqrt {{{\left( {n + 1} \right)} \mathord{\left/ {\vphantom {{\left( {n + 1} \right)} \pi }} \right. \kern-\nulldelimiterspace} \pi }} \varphi \prime \varphi ^n ,n = 0,1, \ldots ,$$ where? is the conformal mapping of the region onto the unit disc. We prove it is dense and determine when it will be a basis. |
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