| Budget Amount *help |
¥1,610,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2006: ¥700,000 (Direct Cost: ¥700,000)
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| Research Abstract |
1. Multilinear singular integrals and Littlewood-Paley operators
We gave a simple proof of a known Lp and Lipschitz estimates about multilinear singular and fractional integrals, and by this new idea we got an extended version of known facts (Article No.2). We got almost final results about existence and boundedness of parametrized Marcinkiewicz integral with rough kernel in Campanato spaces (Article No.1). Introducing some new ideas, we obtained new L2 estimates for Marcinkiewicz integrals along surfaces with variable kernels (Article No.3, 12, 13). We also got weighted estimates for Littlewood-Paley operator (Article No. 14).
2. Singular integrals
About singular integrals on amalgum spaces between Lp and lp, we obtained the same estimates as in the classical case, and gave an application to PDE (Article No. 15). We also got an result about singular integrals along variable surfaces (Article No. 11).
3. About Fourier multipliers and Pseudo differential operators, we also got three results as related theme (Article No.9, 17, 18).
4. Hardy space theory as related theme
We established a transplantation theorem in Hardy spaces for Jacobi polynomials orthogonal series, and we showed an analogy of Burkholder-Gundy-Siverstein's theorem in the weighted Hardy spaces on intervals of the real line (Article No.4, 5, 16). We gave an constructive method of an atomic decomposition of functions with compact support (article No.8).
5. Related function spaces
We showed that one can define predual of generalized Morrey-Campanato spaces in terms of generalized atoms, which extends the known famous Coifman-Weiss result (Article No.19). We also obtain new results on Campanato spaces, Morrey spaces, and Orlitz-Morrey spaces (Article No.6, 10).
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