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Keywords:
generalized shift operator; Riesz-Bessel transformations
generalized shift operator; Riesz-Bessel transformations
Summary:
In this paper, the boundedness of the Riesz potential generated by generalized shift operator $I^{\alpha }_{B_{k}}$ from the spaces ${a = (L_{p_{m}, \nu } (\mathbb{R}_n^k), a_m)}$ to the spaces ${a^{\prime }= (L_{q_{m}, \nu } (\mathbb{R}_n^k), a^{\prime }_m)}$ is examined.
References:
[1] I. A. Aliev: On Riesz transformations generated by a generalized shift operator. Izvestiya Acad. of Sciences of Azerbaydian 1 (1987), 7–13. MR 0939101
[2] I. A. Aliev and A. D. Gadzhiev: Weighted estimates for multidimensional singular integrals generated by the generalized shift operator. Matematika Sbornik Rossiyskaya Akad. Nauk 183 (1992), 45–66 English translation. MR 1198834
[3] W. D. Chang: Boundedness of the Calderon-Zygmund singular integral operators on B$a$ spaces. Proc. Amer. Math. Soc. 109 (1990), 403–408. MR 1007492
[4] W. D. Chang: The boundedness of some integral operators in a new class of function spaces. Acta Math. Sci. 4 (1984), 381–396. MR 0812722
[5] X. Ding and P. Luo: B$a$ spaces and some estimates of Laplace operators. J. Systems Sci. Math. Sci. 1 (1981), 9–33. MR 0820383
[6] Y. Deng and Y. Gu: A new class of function spaces and Hilbert transform. J. Math. Anal. Appl. 108 (1985), 99–106. DOI 10.1016/0022-247X(85)90011-3 | MR 0791136
[7] Y. Deng, W. Chang and Y. Li: On Boundedness of Riesz Transform and the Riesz Potential in B$a$ Spaces, Theory of B$a$ spaces and its applications. Science Press, Beijing, 1999, pp. 63–72. MR 1414957
[8] A. D. Gadzhiev and I. A. Aliev: On a potential like operators generated by the generalized shift operator. Vekua Inst. Applied Math. 3 (1988), 21–24.
[9] I. Ekincioglu and I. Kaya Özkin: On high order Riesz transformations generated by a generalized shift operator. Tr. J. Math. 21 (1997), 51–60. MR 1473300
[10] I. Ekincioglu and A. Serbetci: On the singular integral operators generated by the generalized shift operator. Int. J. App. Math. 1 (1999), 29–38. MR 1689693
[11] B. M. Levitan: Bessel function expansions in series and fourier integrals. Uspekhi Mat. Nauk 6 (1951), 102–143. MR 0049376
[12] E. M. Stein: Singular Integrals and Differentiability Properties of Functions. Princeton Univ. Press, Princeton, N. J., 1970. MR 0290095 | Zbl 0207.13501
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