107
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

On a certain class of spherical harmonic functions and singular pseudo-differential operators

&
Pages 27-38 | Received 03 Nov 2005, Published online: 14 Feb 2007

References

  • Levitan , B. M. 1951 . Bessel function expansions in series and Fourier integrals . Uspekhi Mathematicheskikh Nauk , 6 ( 42 ) : 102 – 143 . No. 2
  • Lyakhov , L. N. 1983 . On a class of spherical functions and singular pseudo-differential operators . Doklady Akademii Naukemii , 28 ( 2 ) : 431 – 434 . 272(4),781–784. (Translation in Soviet Mathematics Doklady
  • Kipriyanov , I. A. 1967 . The Fourier–Bessel transformation and embedding theorems for weighted class . Trudy Matematicheskogo Instituta Steklova , 89 : 130 – 213 .
  • Kipriyanov , I. A. and Klyuchantsev , M. I. 1970 . On singular integrals generated by a generalized shift operator, II . Sibirskii Math. Zhurnal , 11 : 1060 – 1083 . (English translation: In Siberian Mathematical Journal, 11, 787–804.)
  • Lyakhov , L. N. 1985 . Spherical weighted-harmonic functions and singular pseudo-differential operators . Doklady Akademii Nauk , 21 ( 6 ) : 1020 – 1032 . (Translation in Differential Equations 21(6), 693–703.)
  • Aliev , I. A. and Gadjiev , A. D. 1994 . Weighted estimates for multidimensional singular integrals generated by generalized shift operator . Matematicheskii Sbornik , 183 ( 9 ) : 45 – 66 . (1992, English Translation: Russian Academy of Sciences Sbornik Mathematics, 77(1), 37–55.)
  • Ekincioglu , I. and Serbetci , A. 2005 . On weighted estimates of high order Riesz–Bessel transformations generated by a generalized shift operator . Acta Mathematica Sinica, English Series , 21 ( 1 ) : 53 – 64 .
  • Mihlin , S. G. 1977 . Linear Partial Differential Equations , Moscow : Vysshaya Shkola .
  • Bateman , G. and Erdelyi , A. 1953 . Higher Transcendental Functions , Vol. 2 , McGraw-Hill .
  • Kipriyanov , I. A. and Bogachev , B. M. 1980 . Properties of functions from a space with a weight on differentiable manifolds . Trudy Mathematicheskogo Instituta Steklov , 156 : 110 – 120 .
  • Agranovich , M. S. 1965 . Elliptic singular integro-differential operators . Uspekhi Mathematicheskikh Nauk , 20 ( 125 ) : 3 – 120 . No. 5

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.