Abstract
In this paper, the boundedness of the Riesz potential generated by generalized shift operator \(I_{B_k }^\alpha \) from the spaces \(Ba = (L_{p_m ,v} ({\mathbb{R}}_n^k ),a_m )\) to the spaces \((L_{q_m ,v} ({\mathbb{R}}_n^k ,a'_m ))\) is examined.
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References
I. A. Aliev: On Riesz transformations generated by a generalized shift operator. Izvestiya Acad. of Sciences of Azerbaydian 1 (1987), 7-13.
I. A. Aliev and A. D. Gadzhiev: Weighted estimates for multidimensional singular in-tegrals generated by the generalized shift operator. Matematika Sbornik Rossiyskaya Akad. Nauk 183 (1992), 45-66 English translation; Russian Acad. Sci. Sb. Math. 77 (1994), 37-55.
W. D. Chang: Boundedness of the Calderon-Zygmund singular integral operators on Ba spaces. Proc. Amer. Math. Soc. 109 (1990), 403-408.
W. D. Chang: The boundedness of some integral operators in a new class of function spaces. Acta Math. Sci. 4 (1984), 381-396.
X. Ding and P. Luo: Ba spaces and some estimates of Laplace operators. J. Systems Sci. Math. Sci. 1 (1981), 9-33.
Y. Deng and Y. Gu: A new class of function spaces and Hilbert transform. J. Math. Anal. Appl. 108 (1985), 99-106.
Y. Deng, W. Chang and Y. Li: On Boundedness of Riesz Transform and the Riesz Potential in Ba Spaces, Theory of Ba spaces and its applications. Science Press, Beijing, 1999, pp. 63-72.
A. D. Gadzhiev and I. A. Aliev: On a potential like operators generated by the general-ized shift operator. Vekua Inst. Applied Math. 3 (1988), 21-24.
I. Ekincioglu and I. Kaya Özkin: On high order Riesz transformations generated by a generalized shift operator. Tr. J. Math. 21 (1997), 51-60.
I. Ekincioglu and A. Serbetci: On the singular integral operators generated by the gen-eralized shift operator. Int. J. App. Math. 1 (1999), 29-38.
B. M. Levitan: Bessel function expansions in series and fourier integrals. Uspekhi Mat. Nauk 6 (1951), 102-143.
E. M. Stein: Singular Integrals and Differentiability Properties of Functions. Princeton Univ. Press, Princeton, N. J., 1970.
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Serbetci, A., Ekincioğlu, I. Boundedness of Riesz Potential Generated by Generalized Shift Operator on Ba Spaces. Czechoslovak Mathematical Journal 54, 579–589 (2004). https://doi.org/10.1007/s10587-004-6410-z
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DOI: https://doi.org/10.1007/s10587-004-6410-z