Integral transforms, connected with fractional powers of nonhomogeneous differential operators in \(L_ p\)-spaces. (English) Zbl 0853.44003
Summary: Some integral transforms, connected with fractional powers of nonhomogeneous elliptic differential operators with real constant coefficients, are considered in \(L_p\)-spaces. We construct the inversion of these transforms and describe their ranges in terms of approximative inverse operators.
MSC:
44A15 | Special integral transforms (Legendre, Hilbert, etc.) |
26A33 | Fractional derivatives and integrals |
35A22 | Transform methods (e.g., integral transforms) applied to PDEs |
31B10 | Integral representations, integral operators, integral equations methods in higher dimensions |
47B38 | Linear operators on function spaces (general) |
47G10 | Integral operators |
Keywords:
potential-type operators; inversion theorems; hypersingular integrals; approximative inverse operators; integral transforms; fractional powers; elliptic differential operatorsReferences:
[1] | Alisultanova E.D., Izv.Vuzov, Matematika 2 pp 3– (1993) |
[2] | Bateman H., Tables of integral transforms (1954) |
[3] | Lizorkin P.I., Matem.Sbornik 60 pp 325– (1963) |
[4] | Nogin V.A., Differ.Uravnen. 9 pp 1606– (1990) |
[5] | Nogin V.A., On convergence in Lp (Rn) of the hypersingular integrals with homogeneous characteristic 179 (1981) |
[6] | Nogin V.A., Dokl.Akad.Nauk 329 pp 550– (1993) |
[7] | Prudnikov A.P., The special functions (1983) |
[8] | Rubin, B.S. 1988.Acoustic potentials and hypersingular integrals with weighted differences, 5910–B88. VINITI. |
[9] | DOI: 10.1002/mana.19891440111 · Zbl 0714.47024 · doi:10.1002/mana.19891440111 |
[10] | Samko S.G., Matem-Zametki 21 pp 677– (1977) |
[11] | Samko S.G., Matem.Zametki 31 pp 855– (1982) |
[12] | Samko S.G., Hypersingular integrals and their applications (1984) · Zbl 0577.42016 |
[13] | DOI: 10.1080/10652469308819017 · Zbl 0924.44003 · doi:10.1080/10652469308819017 |
[14] | Samko S.G., Studia Mathematica 1 (1994) |
[15] | Samko S.G., Theory and Applications (1993) |
[16] | Zavolzhenskii M.M., Dokl.Akad.Nauk SSSR 324 pp 738– (1992) |
[17] | Zavolzhenskii, M.M. and Nogin, V.A. 1992.Approximative approach to inversion of the potential-type operators with smooth characteristics, 2150–B92. Moscow: VINITI. |
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