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In this paper, we study the generalized Littlewood-Paley operators. It is shown that the generalized g-function, Lusin area function and g∗λ-function on any BMO function are either infinite everywhere, or finite almost everywhere, respectively; and in the latter case, such operators are bounded from BMO(Rn) to BLO(Rn), which improve and generalize some previous results.
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참고문헌 (16)
참고문헌 신청
A. Benedek / 1962 / Convolution operators on Banach space valued functions / Proc. Natl. Acad. Sci. USA 48 (3) : 356 ~ 365
D. Kurtz / 1987 / Littlewood-Paley operators on BMO / Proc. Amer. Math. Soc 99 (4) : 657 ~ 666
E. Stein / 1958 / On the functions of Littlewood-Paley, Lusin, and Marcinkiewicz / Trans. Amer. Math. Soc 88 : 430 ~ 466
E. Stein / 1970 / Singular Integrals and Differentiability Properties of Functions / Princeton Univ. Press
H. Lin / 2011 / Boundedness of Lusin-area and g?λ functions on localized BMO spaces over doubling metric measure spaces / Bull. Sci. Math 135 (1) : 59 ~ 88
D. Kurtz / 1987 / Littlewood-Paley operators on BMO / Proc. Amer. Math. Soc 99 (4) : 657 ~ 666
E. Stein / 1958 / On the functions of Littlewood-Paley, Lusin, and Marcinkiewicz / Trans. Amer. Math. Soc 88 : 430 ~ 466
E. Stein / 1970 / Singular Integrals and Differentiability Properties of Functions / Princeton Univ. Press
H. Lin / 2011 / Boundedness of Lusin-area and g?λ functions on localized BMO spaces over doubling metric measure spaces / Bull. Sci. Math 135 (1) : 59 ~ 88
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