RUS  ENG
Full version
JOURNALS // Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory // Archive

Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 2021 Volume 193, Pages 3–10 (Mi into794)

Boundedness theorem for one class of pseudodifferential equations with degeneration

A. D. Baevab, A. A. Babaitsevb, V. D. Kharchenkob

a Voronezh State University, Faculty of Mathematics
b Voronezh State University

Abstract: In this paper, we prove a boundedness theorem for one class of pseudodifferential equations with degeneration. We consider a new class of variable symbols depending on a complex parameter. Pseudodifferential operators are constructed by a special integral transformation. The boundedness theorem for these operators is proved in special weighted Sobolev-type spaces.

Keywords: pseudodifferential operator with degeneration, boundedness theorem, weighted Sobolev space.

UDC: 517.956

MSC: 35S05

DOI: 10.36535/0233-6723-2021-193-3-10



© Steklov Math. Inst. of RAS, 2024