Buradasınız

FOURIER- BESSEL DÖNÜŞÜM Ü TARAFINDAN ÜRETİLEN p - SEMİGRUBU VE p - SEMİGUP TARAFINDAN DOĞRULAN RİESZ POTANSİYELİ ÜZERİNE

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

Journal Name:

Publication Year:

Abstract (2. Language): 
P - semigroup associated with singular Laplace- Bessel differential operator n—1 ^2 ( ^2 k=1 0Xk d2 2v d X n S X n J is introduced. Representations of the Riesz potentials (—A B) 2 (p , (ReCK > 0) via the P -semigroup are obtained. Mathematics Subject Classification: 26A33, 44A35
Abstract (Original Language): 
Bu çalışmada öncelikle n-1 A B =S- d2 (d2 2v d Xn fan J ..:fa; Laplace- Bessel Diferansiye l operatorü tarafından üretilen P - semigrup tanımlanmıştır. Tanımlanmış olan P - semigrup vasıtasıyla (—A B) 2 p , Riesz potansiyelinin yeni bir gösterimi elde edilmiştir.
175
186

REFERENCES

References: 

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 LLP (RN) 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 LAP R (RN ) 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)
EÜFBED - Fen Bilimleri Enstitüsü Dergisi Cilt-Sayı: 6-2 Yıl: 2013 175-186
186
Keleş ve Bayrakçı
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¬109.
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.

Thank you for copying data from http://www.arastirmax.com