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## Archive of Issues

Russia Rostov-on-Don
Year
2021
Volume
31
Issue
2
Pages
194-209
 Section Mathematics Title The Boutet de Monvel operators in variable Hölder–Zygmund spaces on $\mathbb{R}^{n}_+$ Author(-s) Kryakvin V.D.a, Omarova G.P.a Affiliations Southern Federal Universitya Abstract We consider Green operators from the Boutet de Monvel algebra in the Hölder–Zygmund spaces of variable smoothness on $\overline{\mathbb R}^{n}_+$. The order of smoothness depends on a point in the domain and may take negative values. The sufficient conditions of boundedness of the Boutet de Monvel operators are obtained. Keywords the Boutet de Monvel calculus, Green operator, Hölder–Zygmund space, variable smoothness UDC 517.954 MSC 35S15, 58J40, 58J05 DOI 10.35634/vm210203 Received 12 September 2020 Language English Citation Kryakvin V.D., Omarova G.P. The Boutet de Monvel operators in variable Hölder–Zygmund spaces on $\mathbb{R}^{n}_+$, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2021, vol. 31, issue 2, pp. 194-209. References Beals R. $L_p$ and Hölder estimates for pseudodifferential operators: sufficient conditions, Annales de l'Institut Fourier, 1979, vol. 29, issue 3, pp. 239-260. https://doi.org/10.5802/aif.760 Beals R. $L_p$ and Hölder estimates for pseudodifferential operators: necessary conditions, Harmonic analysis in Euclidean spaces, Providence, R.I.: AMS, 1979, pp. 153-157. Brenner A.V., Shargorodsky E.M. Boundary value problems for elliptic pseudodifferential operators, Partial differential equations. IX, Berlin: Springer, 1997, pp. 145-215. https://doi.org/10.1007/978-3-662-06721-5_2 Eskin G.I. Boundary value problems for elliptic pseudodifferential equations, Providence, R.I.: AMS, 1981. Grubb G. Functional calculus of pseudo-differential boundary problems, Boston: Birkhäuser, 1986, pp. 14-124. https://doi.org/10.1007/978-1-4757-1898-0 Grubb G. Pseudo-differential boundary problems in $L_p$-spaces, Communications in Partial Differential Equations, 1990, vol. 15, issue 3, pp. 289-340. https://doi.org/10.1080/03605309908820688 Hörmander L. The analysis of linear partial differential operators. III. Pseudo-differential operators, Berlin: Springer, 2007. https://doi.org/10.1007/978-3-540-49938-1 Johnsen J. Elliptic boundary problems and the Boutet de Monvel calculus in Besov and Triebel–Lizorkin spaces, Mathematica Scandinavica, 1996, vol. 79, pp. 25-85. https://doi.org/10.7146/math.scand.a-12593 Kryakvin V.D. Boundedness of pseudodifferential operators in Hölder–Zygmund spaces of variable order, Siberian Mathematical Journal, 2014, vol. 55, issue 6, pp. 1073-1083. https://doi.org/10.1134/S0037446614060093 Kryakvin V., Omarova G. Spectral invariance for pseudodifferential operators in Hölder–Zygmund spaces of the variable smoothness, Journal of Pseudo-Differential Operators and Applications, 2018, vol. 9, no. 1, pp. 95-104. https://doi.org/10.1007/s11868-016-0182-8 Kryakvin V., Rabinovich V. Pseudodifferential operators in weighted Hölder–Zygmund spaces of the variable smoothness, Large truncated Toeplitz matrices, Toeplitz operators, and related topics, Cham: Birkhäuser, 2017, pp. 511-531. https://doi.org/10.1007/978-3-319-49182-0_21 Monvel L.B. Boundary problems for pseudo-differential operators, Acta Mathematica, 1971, vol. 126, pp. 11-51. https://doi.org/10.1007/BF02392024 Rempel S., Schulze B.-W. Index theory of elliptic boundary problems, Berlin: Akademie Verlag, 1982. Stein E.M. Harmonic analysis (PMS-43), Princeton: Princeton University Press, 1993. https://doi.org/10.1515/9781400883929 Triebel H. Theory of function spaces, Basel: Birkhäuser, 1983. https://doi.org/10.1007/978-3-0346-0416-1 Full text