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On Weighted Estimates of High-Order Riesz-Bessel Transformations Generated by the Generalized Shift Operator

On Weighted Estimates of High-Order Riesz-Bessel Transformations Generated by the Generalized Shift Operator
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摘要 In this paper, we establish sufficient conditions on weights which ensurethat high-order Riesz-Bessel transformations generated by the generalized shift operator actboundedly from one weighted L_p-space into another. In this paper, we establish sufficient conditions on weights which ensurethat high-order Riesz-Bessel transformations generated by the generalized shift operator actboundedly from one weighted L_p-space into another.
作者 Isman EKINCIOGLU Ayhan SERBETCI
机构地区 Department Department of Mathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2005年第1期53-64,共12页 数学学报（英文版）
关键词 Generalized shift operator Riesz-Bessel transformations Generalized shift operator Riesz-Bessel transformations
分类号 O174 [理学—基础数学]
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参考文献15

  • 1Klyuchantsev, M. I., On singular integrals generated by the generalized shift operator, I.. Sibirsk. Math.Zh., 11,810-821 (1970). English translation: in Siberian Math. J., 11, (1970).
  • 2Kipriyanov, I., A., Klyuchantsev, M. I.: On singular integrals generated by the generalized shift operator,II, Sibirsk. Mat. Zh., 11, 1060-1083 (1970), English translation: in Siberian Math. J., 11, (1970).
  • 3Aliev, I. A., Gadzhiev, A. D.: Weighted Estimates for Multidimensional Singular Integrals Generated by The Generalized Shift Operator. Matematika Sbornik Rossiyskaya Akad. Nauk., 183(9), 45-66 (1992).
  • 4Stein, E. M.: Note on Singular Integrals. Proc. Amer. Math. Sock, 8, 250-254 (1957).
  • 5Dyk'in, E. M., Osilenker, B. P.: Weighted Estimates of Singular Integrals And Applications. J. Soviet Math., 30(3), (1985).
  • 6Maz'ya, V., G.: Sobolev Spaces, Springer-Verlag, Berlin, 1985.
  • 7Stein, E. M.: Singular Integrals And Differentiability Properties of Functions, Princeton Univ. Press,Princeton, N. J., 1970.
  • 8Ekincioglu, I., Serbetci, A.: On the singular integral operators generated by the generalized shift operator.Int. J. App. Math., 1(1), 29-38 (1999).
  • 9Levitan, B. M., Bessel function expansions in series and fourier integrals. Uspekhi Mat. Nauk., 6, no.2(42),102-143 (1951).
  • 10Aliev, I. A.: On Riesz Transformations Generated by A Generalized Shift Operators. Izvestiya Acad. of Sciences of Azerbaydian, 1, 7-13 (1987~.
Acta Mathematica Sinica,English Series
2005年 第1期

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