Geodesic
Boundedness theorem for one class of pseudodifferential equations with degeneration
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 4, Tome 193 (2021), pp. 3-10

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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. 
@article{INTO_2021_193_a0,
     author = {A. D. Baev and A. A. Babaitsev and V. D. Kharchenko},
     title = {Boundedness theorem for one class of pseudodifferential equations with degeneration},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {3--10},
     publisher = {mathdoc},
     volume = {193},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_193_a0/}
}
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A. D. Baev; A. A. Babaitsev; V. D. Kharchenko. Boundedness theorem for one class of pseudodifferential equations with degeneration. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 4, Tome 193 (2021), pp. 3-10. http://geodesic.mathdoc.fr/item/INTO_2021_193_a0/