Taiwanese Journal of Mathematics


Yanchang Han

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Using the discrete Calderón reproducing formula in [9] and the Plancherel-Pôlya characterization of the inhomogeneous Besov and Triebel-Lizorkin spaces developed in [5], we prove pointwise multipliers on inhomogeneous Besov and Triebel-Lizorkin spaces in the setting of spaces of homogeneous type.

Article information

Taiwanese J. Math., Volume 17, Number 1 (2013), 179-206.

First available in Project Euclid: 10 July 2017

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Primary: 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems
Secondary: 42B25: Maximal functions, Littlewood-Paley theory 42B35: Function spaces arising in harmonic analysis

pointwise multiplier multiplication operator Besov and Triebel-Lizorkin space Calderón reproducing formula space of homogeneous type


Han, Yanchang. POINTWISE MULTIPLIERS ON INHOMOGENEOUS BESOV AND TRIEBEL-LIZORKIN SPACES IN THESETTING OF SPACES OF HOMOGENEOUS TYPE. Taiwanese J. Math. 17 (2013), no. 1, 179--206. doi:10.11650/tjm.17.2013.1864. https://projecteuclid.org/euclid.twjm/1499705882

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  • M. Christ, A $T(b)$ theorem with remarks on analytic capacity and the Cauchy integral, Colloq. Math., 60/61 (1990), 601-628.
  • R. R. Coifman and G. Weiss, Analyse harmonique noncommutative sur certains espaces homogenes, Lecture Notes in Math., Vol. 242, Springer-Verlag, Berlin and New York, 1971.
  • G. David, J. L. Journé and S. Semmes, Operateurs de Calderón-Zygmund, Fonction Para-accretive et Interpolation, Rev. Mat. Iberoamericanna, 1 (1985), 1-56.
  • D. G. Deng and Y. S. Han, Harmonic analysis on spaces of homogeneous type, Lecture notes in mathematics, Springer, 2009.
  • D. G. Deng, Y. S. Han and D. C. Yang, Inhomogeneous Plancherel-Pôlya type inequanlity on spaces of homogeneous type and their applications, Communications in Contemporary Mathematics, 6(2) (2004), 221-243.
  • C. Feferman and E. M. Stein, Some maximal inequalities, Amer. J. Math., 93 (1971), 107-115.
  • M. Frazier and B. Jawerth, A discrete transform and decompositions of distribution spaces, J. Funct. Anal., 93 (1990), 34-170.
  • N. S. Feldman, Pointwise multipliers from the Hardy space to the Bergman space, Illinois J. Math., 43 (1999), 211-221.
  • Y. S. Han, S. Z. Lu and D. C. Yang, Inhomogeneous discrete Calderón reproducing formulas for spaces of homogeneous type, J. Fourier Anal. Appl., 7 (2001), 571-600.
  • Y. S. Han and E. T. Sawyer, Littlewood-Paley theory on spaces of homogeneous type and classical function spaces, Mem. Amer. Math. Soc., 110 (1994), 1-126.
  • Y. S. Han and D. C. Yang, Some new spaces of Besov and Triebel-Lizorkin type on homogeneous spaces, Studia Mathematica, 156 (2003), 67-97.
  • K. Herbert and S. Winfried, Pointwise multipliers of Besov spaces of smoothness zero and spaces of continuous functions, Rev. Mat. Iberoamericana, 18 (2002), 587-626.
  • R. A. Macias and C. Segovia, Lipschitz function on spaces of homogeneous type, Adv. Math., 33 (1979), 257-270.
  • V. G. Mazya and T. O. Shaposhnikova, Theory of Sobolev multipliers, Grundlehren der Mathematischen Wissenschaften, 337. Springer, Berlin, 2009.
  • E. Nakai and K. Yabuta, Pointwise multipliers for functions of bounded mean oscillation, J. Math. Soc. Japan, 37 (1985), 207-218.
  • T. Runst and W. Sickel, Sobolev spaces of fractional order, Nemytskij operators, and nonlinear partial differential equations, Berlin, W. de Gruyter, 1996.
  • W. Sickel, On pointwise multipliers for $F_{p}^{s,q}(\mathbb{R}^d)$ in case $\sigma_{p,q}< s < \frac{n}{p}$, Ann. Mat. Pura Appl., IV. Ser., 176 (1999), 209-250.
  • R. S. Strichartz, Multipliers on fractional Sobolev spaces, J. Math. Mech., 16 (1967), 1031-1060.
  • H. Triebel, Theory of function spaces, Monographs in mathematics, 78, Birkhäuser, Basel, 1983.
  • K. Yabuta, Pointwise Multipliers of Weighted BMO Spaces, Proceedings of the American Mathematical, 117 (1993), 737-744.