New classes of function spaces and singular operators. (English. Russian original) Zbl 1507.47103
Trans. Mosc. Math. Soc. 2021, 273-288 (2021); translation from Tr. Mosk. Mat. O.-va 82, No. 2, 329-348 (2021).
Summary: This article is dedicated to the memory of Garnik Al’bertovich Karapetyan and it contains a review of results obtained by G. A. Karapetyan and his colleagues within the joint Russian-Armenian project of RFBR. In the first section, we look at multi-anisotropic spaces which were intensively studied by Karapetyan and his students. The second section is devoted to a new class of singular Hausdorff and Hausdorff-Berezin operators. In the third section, we study the connection between real function spaces and operator algebras in a Hilbert space, established by means of a quantization procedure.
MSC:
| 47G10 | Integral operators |
| 26C05 | Real polynomials: analytic properties, etc. |
| 47B10 | Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.) |
| 47-03 | History of operator theory |
| 01A72 | Schools of mathematics |
Keywords:
semielliptic operator; Noether operator; generalised homogeneous polynomial; Newton polytope; multi-anisotropic Sobolev space; multi-anisotropic spaces; embedding theorems; Hausdorff operators; Hausdorff-Berezin operators; Schatten classes; Hilbert-Schmidt operators; Riesz operatorsBiographic References:
Karapetyan, Garnik Al’bertovichReferences:
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