Taiwanese Journal of Mathematics

ON WEAK TYPE BOUNDS FOR A FRACTIONAL INTEGRAL ASSOCIATED WITH THE BESSEL DIFFERENTIAL OPERATOR

Mehmet Zeki Sarikaya and H¨useyin Yildirim

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Abstract

In this study we show that $I_{\Omega ,\alpha ,v}$ and $M_{\Omega ,\alpha ,v},$ the fractional integral and maximal operators the generalized shift operator generated by Bessel differential operator respectively, are bounded operators from $L_{1,v}\left( \left\vert x\right\vert ^{\frac{\beta (n+2\left\vert v\right\vert -\alpha )}{n+2\left\vert v\right\vert }}\right. ,$ $\left.\mathbb{R}_{n}^{+}\right) $ to $L_{\frac{n+2\left\vert v\right\vert }{n+2\left\vert v\right\vert -\alpha },\infty }\left( \left\vert x\right\vert ^{\beta }, \mathbb{R}_{n}^{+}\right) $ where $0\lt \alpha 0,...,v_{n}\gt 0,\left\vert v\right\vert =v_{1}+...+v_{n}$and $-1\lt \beta \lt 0.$.

Article information

Source
Taiwanese J. Math., Volume 12, Number 9 (2008), 2535-2548.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405194

Digital Object Identifier
doi:10.11650/twjm/1500405194

Mathematical Reviews number (MathSciNet)
MR2479070

Zentralblatt MATH identifier
1170.31301

Subjects
Primary: 31B10: Integral representations, integral operators, integral equations methods 44A15: Special transforms (Legendre, Hilbert, etc.) 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)

Keywords
Bessel differential operator maximal operator and fractional integral

Citation

Sarikaya, Mehmet Zeki; Yildirim, H¨useyin. ON WEAK TYPE BOUNDS FOR A FRACTIONAL INTEGRAL ASSOCIATED WITH THE BESSEL DIFFERENTIAL OPERATOR. Taiwanese J. Math. 12 (2008), no. 9, 2535--2548. doi:10.11650/twjm/1500405194. https://projecteuclid.org/euclid.twjm/1500405194


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References

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