Abstract
A generalized paraproduct
is defined, where S t , T t are non-convolution operator families. The main result is that Π b (f) is bounded on L 2(R n) provided b ε BMO (R n).
Keywords
- Hardy Space
- Singular Integral Operator
- Continuous Linear Operator
- Homogeneous Type
- Zygmund Operator
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References
M. Christ and J.-L. Journé, Estimates for multilinear singular integral operators with polynomial growth. Acta Mathematica, 159 (1987), 51–80.
R. Coifman and Y. Meyer, Au-dela des opérateurs pseudo-différentiels, Astérisque, 57(1980).
R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bul. of AMS, vol. 83, 4 (1977), 569–645.
G. David and J.-L. Journé, A boundedness criterion for generalized Calderón-Zygmund operators, Ann. of Math., vol. 120 (1984), 371–197.
C. Fefferman and E. M. Stein, H p spaces of several variables, Acta Math., 129(1972), 137–193.
A. Macias and C. Segovia, Segovia, Lipschitz functions on spaces of homogeneous type, Advances in Math., 33(1979), 257–270.
A. Macias and C. Segovia, A decomposition into atoms of distributions on spaces of homogeneous type, Advances in Math., 33(1979), 271–309.
Y. Meyer, Minimalité de certains espaces fonctionnels et applications à la théorie des opérateurs, Preprint.
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© 1991 Springer-Verlag
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Deng, Dg., Han, Y. (1991). On a generalized paraproduct defined by non-convolution. In: Cheng, MT., Deng, DG., Zhou, XW. (eds) Harmonic Analysis. Lecture Notes in Mathematics, vol 1494. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087755
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DOI: https://doi.org/10.1007/BFb0087755
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-54901-7
Online ISBN: 978-3-540-46474-7
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