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In this paper, we show that the commutator of the intrinsic square function with {\rm BMO} symbols is bounded on the variable exponent Lebesgue spaces $L^{p(\cdot)}(\mathbb{R}^n)$ applying a generalization of the classical Rubio de Francia extrapolation. As a consequence we further establish its boundedness on the variable exponent Morrey spaces $\mathcal{M}_{p(\cdot), u}$, Morrey-Herz spaces $M\dot{K}_{q, p(\cdot)}^{\alpha(\cdot), \lambda}({\mathbb { R}}^n)$ and Herz type Hardy spaces $H\dot{K}_{p(\cdot)}^{\alpha(\cdot), q}({\mathbb { R}}^n)$, where the exponents $\alpha(\cdot)$ and $p(\cdot)$ are variable. Observe that, even when $\alpha(\cdot)\equiv \alpha$ is constant, the corresponding main results are completely new.
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참고문헌 (45)
참고문헌 신청
A. Almeida / 2012 / Maximal, potential and singular type operators on Herz spaces with variable exponents / J. Math. Anal. Appl. 394(2):781~795
Y. Chen / 2006 / Variable exponent, linear growth functionals in image restoration / SIAM J. Appl. Math. 66(4):1383~1406
D. V. Cruz-Uribe / 2013 / Variable Lebesgue Spaces, Applied and Numerical Harmonic Analysis / Birkhauser, Springer
D. Cruz-Uribe / 2003 / The maximal function on variable $L^p$ spaces / Ann. Acad. Sci. Fenn. Math. 28(1):223~238
D. Cruz-Uribe / 2006 / The boundedness of classical operators on variable $L^p$ spaces / Ann. Acad. Sci. Fenn. Math. 31(1):239~264
Y. Chen / 2006 / Variable exponent, linear growth functionals in image restoration / SIAM J. Appl. Math. 66(4):1383~1406
D. V. Cruz-Uribe / 2013 / Variable Lebesgue Spaces, Applied and Numerical Harmonic Analysis / Birkhauser, Springer
D. Cruz-Uribe / 2003 / The maximal function on variable
D. Cruz-Uribe / 2006 / The boundedness of classical operators on variable
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