BibTex RIS Kaynak Göster

-

Yıl 2013, Cilt: 6 Sayı: 2, 175 - 186, 18.03.2014

Öz

 - semigroup associated with singular Laplace- Bessel differential operator                  n n n  is introduced. Representations of the Riesz potentials        B ,   Re   via the  -semigroup are obtained. Mathematics Subject Classification: 26A33, 44A35

Kaynakça

  • Levitan, B. M., (1951), Bessel function expansions in series and Fourier Integrals, Uspekhi Mat. Nauk 6, No 2, 102-143 ( In Russian).
  • Stein, E. M., (1961), The characterization of functions arising as potentials, Bull. Amer. Math. Soc., 67, No 1, 101-104.
  • Muckenhoupt, B., Stein, E., (1965), Classical expansions and their relation to conjugate harmonic functions, Trans. Amer. Mat. Soc., 118, 17-92.
  • Kipriyanov, I. A., (1967), The Fourier Bessel Transformation and embedding theorems for weighted class, Trudy Mat. Inst. AN SSSR, 89, 130-213. ( In Russian)
  • Wheeden, R. L., (1969), On hypersingular Integrals and Lebesgue Spaces of differentiable functions, II. Trans. Amer. Math. Soc., 139, No 1, 37-53. Lizorkin, P. I., (1970), On description of   n r p R L space in the term of difference singular integrals, Math. Sbornik, 81, No 1, 79-91.
  • Stein, E. M., (1970), Singular integrals and differentiability Properties of Functions, Princeton Univ., Press, Princeton, N. J.
  • Kipriyanov, I. A., Klyuchantsev, M. I., (1970), On Singular Integrals generated by the generalized shift operator, II. Sibirsk. Mat. Zh. 11, 1060-1083 ( In Russian); English translate in: Siberian Math. J. 11
  • Klyuchantsev, M. I.,(1970), On Singular integrals generated by the generalized shift operator, I. Sibirsk. Mat. Zh. 11, 810-821 ( In Russian)
  • Fisher, M. J., (1971), Singular Integrals and fractional powers of operators, Trans. Amer. Math. Soc., 161, No 2, 307-326.
  • Samko, S. G. (1976), On Riesz potentials spaces, Izv. AN SSSR (Ser. Mat.), 40, No 5, 1143-1172.
  • Samko, S. G., (1977), The spaces   n r p R L  , and the hypersingular integrals, Stud. Math. (PRL), 61, No 3, 193-230.
  • Lyakhov, L. N., (1984), On classes of spherical functions and singular psedodifferential operators, Dokl. Akad Nauk 272, 781-784 ( In Russian)
  • Samko, S. G., Kilbas, A. A., Marichev, O.I., (1987), Integrals and derivatives of fractional order and some of their applications, Nauk. Tek., Minsk. Aliev, I. A., (1987), Riesz transform generated by a generalized shift operator, Izvestiya Akad Nauk Azaerbaijan Rep. ( Ser. Fiz. Techn. Math. Nauk) 1, 7-13 ( In Russian)
  • Gadjiev, A. D., Aliev, I. A., (1988), The Riesz and Bessel type potentails generated by a generalized shift operator and their inverse, Proc. IV All- Union Winter Conf., Theory of functions and Approximation, 47-53, Saratov.
  • Gadjiev, A. D., Aliev, I. A., (1988), On a class of potential type operator generated by a generalized shift operator, Reports Seminar of the I. N. Vekua Inst., Appl. Math., 3, No 2, Tbilisi.
  • Aliev, I. A., Gadjiev, A. D., (1994), Weighted estimates of multidimensional singular integrals generated by the generalized shift operator, Russian Acad. Sci. Sb. Math. 77, No 1, 37-55.
  • Rubin, B. S., (1996), Fractional Integrals and Potentials, Essex- U. K., Addison Wesley- Longman.
  • Guliyev, V. S. (1998), Sobolev’s theorem for Riesz B- Potentials, Dokl. Rus. Akad. Nauk, 358, No 4, 450-451.
  • Mourou, M. A., Trimeche, K., (1998), Calderon’s reproducing formula associated with the Bessel operator, J. Math. Anal. and Appl 219, 97
  • Bayrakci S., Aliev, I. A., (1998), On inversion of B- elliptic potentials by the method of Balakrishnan- Rubin, Fractioanl Calculus and Applies Analysis, Vol 1, No 4, 365-384.
  • Sezer, S., Aliev, I. A., (2010), A new characterization of the Riesz potential spaces with the aid of a composite wavelet transform, Journal of Mathematical Analysis and Applications, 372, 549-558. ****

ON  SEMIGROUP GENERATED BY FOURIER- BESSEL TRANSFORM AND RIESZ POTENTIAL ASSOCIATED WITH   SEMIGROUP

Yıl 2013, Cilt: 6 Sayı: 2, 175 - 186, 18.03.2014

Öz

- semigroup associated with singular Laplace- Bessel differential operator

 

is introduced. Representations of the Riesz potentials ,  via the -semigroup are obtained.

 

Mathematics Subject Classification: 26A33, 44A35

Kaynakça

  • Levitan, B. M., (1951), Bessel function expansions in series and Fourier Integrals, Uspekhi Mat. Nauk 6, No 2, 102-143 ( In Russian).
  • Stein, E. M., (1961), The characterization of functions arising as potentials, Bull. Amer. Math. Soc., 67, No 1, 101-104.
  • Muckenhoupt, B., Stein, E., (1965), Classical expansions and their relation to conjugate harmonic functions, Trans. Amer. Mat. Soc., 118, 17-92.
  • Kipriyanov, I. A., (1967), The Fourier Bessel Transformation and embedding theorems for weighted class, Trudy Mat. Inst. AN SSSR, 89, 130-213. ( In Russian)
  • Wheeden, R. L., (1969), On hypersingular Integrals and Lebesgue Spaces of differentiable functions, II. Trans. Amer. Math. Soc., 139, No 1, 37-53. Lizorkin, P. I., (1970), On description of   n r p R L space in the term of difference singular integrals, Math. Sbornik, 81, No 1, 79-91.
  • Stein, E. M., (1970), Singular integrals and differentiability Properties of Functions, Princeton Univ., Press, Princeton, N. J.
  • Kipriyanov, I. A., Klyuchantsev, M. I., (1970), On Singular Integrals generated by the generalized shift operator, II. Sibirsk. Mat. Zh. 11, 1060-1083 ( In Russian); English translate in: Siberian Math. J. 11
  • Klyuchantsev, M. I.,(1970), On Singular integrals generated by the generalized shift operator, I. Sibirsk. Mat. Zh. 11, 810-821 ( In Russian)
  • Fisher, M. J., (1971), Singular Integrals and fractional powers of operators, Trans. Amer. Math. Soc., 161, No 2, 307-326.
  • Samko, S. G. (1976), On Riesz potentials spaces, Izv. AN SSSR (Ser. Mat.), 40, No 5, 1143-1172.
  • Samko, S. G., (1977), The spaces   n r p R L  , and the hypersingular integrals, Stud. Math. (PRL), 61, No 3, 193-230.
  • Lyakhov, L. N., (1984), On classes of spherical functions and singular psedodifferential operators, Dokl. Akad Nauk 272, 781-784 ( In Russian)
  • Samko, S. G., Kilbas, A. A., Marichev, O.I., (1987), Integrals and derivatives of fractional order and some of their applications, Nauk. Tek., Minsk. Aliev, I. A., (1987), Riesz transform generated by a generalized shift operator, Izvestiya Akad Nauk Azaerbaijan Rep. ( Ser. Fiz. Techn. Math. Nauk) 1, 7-13 ( In Russian)
  • Gadjiev, A. D., Aliev, I. A., (1988), The Riesz and Bessel type potentails generated by a generalized shift operator and their inverse, Proc. IV All- Union Winter Conf., Theory of functions and Approximation, 47-53, Saratov.
  • Gadjiev, A. D., Aliev, I. A., (1988), On a class of potential type operator generated by a generalized shift operator, Reports Seminar of the I. N. Vekua Inst., Appl. Math., 3, No 2, Tbilisi.
  • Aliev, I. A., Gadjiev, A. D., (1994), Weighted estimates of multidimensional singular integrals generated by the generalized shift operator, Russian Acad. Sci. Sb. Math. 77, No 1, 37-55.
  • Rubin, B. S., (1996), Fractional Integrals and Potentials, Essex- U. K., Addison Wesley- Longman.
  • Guliyev, V. S. (1998), Sobolev’s theorem for Riesz B- Potentials, Dokl. Rus. Akad. Nauk, 358, No 4, 450-451.
  • Mourou, M. A., Trimeche, K., (1998), Calderon’s reproducing formula associated with the Bessel operator, J. Math. Anal. and Appl 219, 97
  • Bayrakci S., Aliev, I. A., (1998), On inversion of B- elliptic potentials by the method of Balakrishnan- Rubin, Fractioanl Calculus and Applies Analysis, Vol 1, No 4, 365-384.
  • Sezer, S., Aliev, I. A., (2010), A new characterization of the Riesz potential spaces with the aid of a composite wavelet transform, Journal of Mathematical Analysis and Applications, 372, 549-558. ****
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Bölüm Makaleler
Yazarlar

Şeyda Keleş

Simten Bayrakçı Bu kişi benim

Yayımlanma Tarihi 18 Mart 2014
Yayımlandığı Sayı Yıl 2013 Cilt: 6 Sayı: 2

Kaynak Göster

APA Keleş, Ş., & Bayrakçı, S. (2014). ON  SEMIGROUP GENERATED BY FOURIER- BESSEL TRANSFORM AND RIESZ POTENTIAL ASSOCIATED WITH   SEMIGROUP. Erzincan University Journal of Science and Technology, 6(2), 175-186.