## Taiwanese Journal of Mathematics

### WEIGHTED LIPSCHITZ ESTIMATES FOR COMMUTATORS OF FRACTIONAL INTEGRALS WITH HOMOGENEOUS KERNELS

#### Abstract

In this paper the authors give a sufficient condition such that the commutator generated by the weighted Lipschitz function and the fractional integral operator with homogeneous kernel satisfying certain Dini condition is bounded on weighted Lebesgue spaces.

#### Article information

Source
Taiwanese J. Math., Volume 15, Number 6 (2011), 2689-2700.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500406491

Digital Object Identifier
doi:10.11650/twjm/1500406491

Mathematical Reviews number (MathSciNet)
MR2896138

Zentralblatt MATH identifier
1258.42015

#### Citation

Lin, Yan; Liu, Zongguang; Pan, Guixia. WEIGHTED LIPSCHITZ ESTIMATES FOR COMMUTATORS OF FRACTIONAL INTEGRALS WITH HOMOGENEOUS KERNELS. Taiwanese J. Math. 15 (2011), no. 6, 2689--2700. doi:10.11650/twjm/1500406491. https://projecteuclid.org/euclid.twjm/1500406491

#### References

• S. Chanillo, A note on commutators, Indiana Univ. Math. J., 31 (1982), 7-16.
• S. Chanillo, D. Watson and R. L. Wheeden, Some integral and maximal operators related to star like sets, Studia Math., \bf107 (1993), 223-255.
• Y. Ding and S. Z. Lu, Weighted norm inequalities for fractional integral operators with rough kernel, Can. J. Math., \bf50 (1998), 29-39.
• Y. Ding and S. Z. Lu, Homogeneous fractional integrals on Hardy spaces, Tohoku Math. J., \bf52 (2000), 153-162.
• J. Duoandikoetxea, Fourier analysis, American Mathematical Society Providence, Rnode Isiana, USA, 1995.
• J. Garc\ipzz a-Cuerva, Weighted $H^{p}$ space, Dissert. Math., \bf162 (1979).
• J. Garc\ipzz a-Cuerva and J. L. Rubio de Francia, Weighed norm inequalities and related topics, North-Holland, Amsterdam, The Netherlands, 1985.
• Y. S. Han, Methods of modern harmonic analysis and their applications, Science Press, Beijing, P. R. China, 1988.
• B. Hu and J. J. Gu, Necessary and sufficient conditions for boundedness of some commutators with weighted Lipschitz functions, J. Math. Anal. Appl., \bf340 (2008), 598-605.
• B. Muckenhoupt and R. L. Wheeden, Weighted norm inequalities for fractional integrals, Trans. Amer. Math. Soc., \bf192 (1974), 261-274.
• M. Paluszyński, Characterization of the Besov spaces via the commutator operator of Coifman, Rochberg and Weiss, Indiana Univ. Math. J., \bf44 (1995), 1-17.
• A. Torchinsky, Real-variable methods in harmonic analysis, Academic Press, New York, USA, 1986.