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In this note we prove that several classes of Littlewood-Paley square operators defined by the kernels without any regularity are bounded on Triebel-Lizorkin spaces $F_\alpha^{p,q}(\mathbb{R}^n)$ and Besov spaces $B_\alpha^{p,q}(\mathbb{R}^n)$ for $0<\alpha<1$ and $1<p,q<\infty$.
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참고문헌 (20)
참고문헌 신청
H. Al-Qassem / 2009 / On certain estimates for Marcinkiewicz integrals and extrapolation / Collect. Math. 60(2):123~145
A. Benedek / 1962 / Convolution operators on Banach space valued functions / Proc. Nat. Acad. Sci. U.S.A. 48(3):356~365
L. C. Cheng / 2007 / On Littlewood-Paley functions / Proc. Amer. Math. Soc. 135(10):3241~3247
Y. Ding / 2000 / On Littlewood-Paley functions and singular integrals / Hokkaido Math. J. 29(3):537~552
Y. Ding / 2016 / Littlewood-Paley functions on homogeneous groups / Forum Math. 28(1):43~55
A. Benedek / 1962 / Convolution operators on Banach space valued functions / Proc. Nat. Acad. Sci. U.S.A. 48(3):356~365
L. C. Cheng / 2007 / On Littlewood-Paley functions / Proc. Amer. Math. Soc. 135(10):3241~3247
Y. Ding / 2000 / On Littlewood-Paley functions and singular integrals / Hokkaido Math. J. 29(3):537~552
Y. Ding / 2016 / Littlewood-Paley functions on homogeneous groups / Forum Math. 28(1):43~55
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