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. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
