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1996 | 119 | 3 | 219-246
Tytuł artykułu

A maximal function characterization of weighted Besov-Lipschitz and Triebel-Lizorkin spaces.

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Abstrakty
EN
We give characterizations of weighted Besov-Lipschitz and Triebel-Lizorkin spaces with $A_∞$ weights via a smooth kernel which satisfies "minimal" moment and Tauberian conditions. The results are stated in terms of the mixed norm of a certain maximal function of a distribution in these weighted spaces.
Twórcy
autor
  • Department of Mathematics, Washington University, St. Louis, Missouri 63130, U.S.A., mitch@math.wustl.edu
Bibliografia
  • [1] H.-Q. Bui, Weighted Besov and Triebel-Lizorkin spaces: Interpolation by the real method, Hiroshima Math. J. 12 (1982), 581-605.
  • [2] H.-Q. Bui, Characterizations of weighted Besov and Triebel-Lizorkin spaces via temperatures, J. Funct. Anal. 55 (1984), 39-62.
  • [3] H.-Q. Bui, Weighted Young's inequality and convolution theorems on weighted Besov spaces, Math. Nachr. 170 (1994), 25-37.
  • [4] H.-Q. Bui, M. Paluszyński and M. H. Taibleson, A note on the Besov-Lipschitz and Triebel-Lizorkin spaces, in: Contemp. Math. 189, Amer. Math. Soc., 1995, 95-101.
  • [5] A. P. Calderón and A. Torchinsky, Parabolic maximal functions associated with a distribution, I, II, Adv. in Math. 16 (1975), 1-64; 24 (1977), 101-171.
  • [6] C. Fefferman and E. M. Stein, $H^p$ spaces of several variables, Acta Math. 129 (1972), 137-193.
  • [7] M. Frazier and B. Jawerth, A discrete transform and decomposition of distribution spaces, J. Funct. Anal. 93 (1990), 34-170.
  • [8] N. J. H. Heideman, Duality and fractional integration in Lipschitz spaces, Studia Math. 50 (1974), 65-85.
  • [9] S. Janson and M. H. Taibleson, I teoremi di rappresentazione di Calderón, Rend. Sem. Mat. Univ. Politec. Torino 39 (1981), 27-35.
  • [10] V. M. Kokilašvili [V. M. Kokilashvili], Maximal inequalities and multipliers in weighted Triebel-Lizorkin spaces, Soviet Math. Dokl. 19 (1978), 272-276.
  • [11] J. Peetre, On spaces of Triebel-Lizorkin type, Ark. Mat. 13 (1975), 123-130.
  • [12] J.-O. Strömberg and A. Torchinsky, Weighted Hardy Spaces, Springer, Berlin, 1989.
  • [13] H. Triebel, Theory of Function Spaces, Birkhäuser, Basel, 1983.
  • [14] H. Triebel, Characterizations of Besov-Hardy-Sobolev spaces: A unified approach, J. Approx. Theory 52 (1988), 162-203.
  • [15] H. Triebel, Theory of Function Spaces II, Birkhäuser, Basel, 1992.
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Bibliografia
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bwmeta1.element.bwnjournal-article-smv119i3p219bwm
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