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Many-dimensional operators of convolution type in spaces of weight-integrable functions
V. S. Rabinovich Rostov State University
Abstract:
We show that a convolution operator in the weight space $L_p^{\langle b\rangle}$ is similar to a generalized convolution operator in $L_p$. We obtain necessary and sufficient conditions for an operator of convolution type, acting in a weight space, to have the Noether property in a cone. These conditions say, in effect, that the operator symbol must not degenerate on the hull of some tubular domain associated with the weight and the cone.
Received: 19.03.1973
Citation:
V. S. Rabinovich, “Many-dimensional operators of convolution type in spaces of weight-integrable functions”, Mat. Zametki, 16:2 (1974), 267–276; Math. Notes, 16:2 (1974), 747–752
Linking options:
https://www.mathnet.ru/eng/mzm7459 https://www.mathnet.ru/eng/mzm/v16/i2/p267
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Abstract page: | 216 | Full-text PDF : | 120 | First page: | 1 |
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