Journal
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS
Volume 23, Issue 4, Pages 919-990Publisher
SPRINGER BIRKHAUSER
DOI: 10.1007/s00041-016-9483-9
Keywords
Metric measure space of homogeneous type; Product; Hardy space; BMO(chi); Regular wavelet; Spline function; Bilinear operator; Paraproduct
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Funding
- National Natural Science Foundation of China [11571039, 11361020]
- Fundamental Research Funds for the Central Universities of China [2016JBM065]
- General Financial Grant from the China Postdoctoral Science Foundation [2016M590037]
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Let be a metric measure space of homogeneous type in the sense of R. R. Coifman and G. Weiss and be the atomic Hardy space. Via orthonormal bases of regular wavelets and spline functions recently constructed by P. Auscher and T. Hytonen, the authors prove that the product of and , viewed as a distribution, can be written into a sum of two bounded bilinear operators, respectively, from into and from into , which affirmatively confirms the conjecture suggested by A. Bonami and F. Bernicot (This conjecture was presented by Ky in J Math Anal Appl 425:807-817, 2015).
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