On the littlewood-paley and lusin functions in higher dimensions.
نویسنده
چکیده
منابع مشابه
Littlewood-Paley Operators on Morrey Spaces with Variable Exponent
By applying the vector-valued inequalities for the Littlewood-Paley operators and their commutators on Lebesgue spaces with variable exponent, the boundedness of the Littlewood-Paley operators, including the Lusin area integrals, the Littlewood-Paley g-functions and g μ *-functions, and their commutators generated by BMO functions, is obtained on the Morrey spaces with variable exponent.
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The aim of this paper is to establish the vector-valued inequalities for Littlewood-Paley operators, including the Lusin area integrals, the Littlewood-Paley g-functions and g∗μ-functions, and their commutators on the Herz-Morrey spaces with variable exponentMK̇ p,q(·)(R n). By applying the properties of Lp(·)(Rn) spaces and the vector-valued inequalities for Littlewood-Paley operators and their...
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We are concerned with Hardy and BMO spaces of operator-valued functions analytic in the unit disk of C. In the case of the Hardy space, we involve the atomic decomposition since the usual argument in the scalar setting is not suitable. Several properties (the Garsia-norm equivalent theorem, Carleson measure, and so on) of BMOA spaces are extended to the operator-valued setting. Then, the operat...
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We extend work of the author to show that the “intrinsic” square function, which pointwise dominates (and, in almost all ways, is easier to work with than) the familiar Lusin area function and its real-variable analogues, also defines a bounded operator on L(R, w dx) for all weights w in the Muckenhoupt Ap class (1 < p < ∞). We apply this result to get a strong weighted Littlewood-Paley inequal...
متن کاملMultilinear commutators of vector-valued intrinsic square functions on vector-valued generalized weighted Morrey spaces
In this paper, we will obtain the strong type and weak type estimates for vector-valued analogs of intrinsic square functions in the generalized weighted Morrey spacesM w (l2). We study the boundedness of intrinsic square functions including the Lusin area integral, the Littlewood-Paley g-function and gλ -function, and their multilinear commutators on vector-valued generalized weighted Morrey s...
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عنوان ژورنال:
- Proceedings of the National Academy of Sciences of the United States of America
دوره 57 1 شماره
صفحات -
تاریخ انتشار 1967