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

H.-Q. Bui; M. Paluszyński; M. Taibleson

Studia Mathematica (1996)

  • Volume: 119, Issue: 3, page 219-246
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Bui, H.-Q., Paluszyński, M., and Taibleson, M.. "A maximal function characterization of weighted Besov-Lipschitz and Triebel-Lizorkin spaces.." Studia Mathematica 119.3 (1996): 219-246. <http://eudml.org/doc/216297>.

@article{Bui1996,
abstract = {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.},
author = {Bui, H.-Q., Paluszyński, M., Taibleson, M.},
journal = {Studia Mathematica},
keywords = {Besov-Lipschitz space; Triebel-Lizorkin space; Littlewood-Paley function; Calderón representation theorem; $A_∞$ weight; Calderón representation; weighted Triebel-Lizorkin spaces; weights; space of test functions; space of tempered distributions; weighted homogeneous Besov-Lipschitz spaces; maximal function of Peetre and Triebel},
language = {eng},
number = {3},
pages = {219-246},
title = {A maximal function characterization of weighted Besov-Lipschitz and Triebel-Lizorkin spaces.},
url = {http://eudml.org/doc/216297},
volume = {119},
year = {1996},
}

TY - JOUR
AU - Bui, H.-Q.
AU - Paluszyński, M.
AU - Taibleson, M.
TI - A maximal function characterization of weighted Besov-Lipschitz and Triebel-Lizorkin spaces.
JO - Studia Mathematica
PY - 1996
VL - 119
IS - 3
SP - 219
EP - 246
AB - 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.
LA - eng
KW - Besov-Lipschitz space; Triebel-Lizorkin space; Littlewood-Paley function; Calderón representation theorem; $A_∞$ weight; Calderón representation; weighted Triebel-Lizorkin spaces; weights; space of test functions; space of tempered distributions; weighted homogeneous Besov-Lipschitz spaces; maximal function of Peetre and Triebel
UR - http://eudml.org/doc/216297
ER -

References

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  1. [1] H.-Q. Bui, Weighted Besov and Triebel-Lizorkin spaces: Interpolation by the real method, Hiroshima Math. J. 12 (1982), 581-605. Zbl0525.46023
  2. [2] H.-Q. Bui, Characterizations of weighted Besov and Triebel-Lizorkin spaces via temperatures, J. Funct. Anal. 55 (1984), 39-62. Zbl0636.46040
  3. [3] H.-Q. Bui, Weighted Young's inequality and convolution theorems on weighted Besov spaces, Math. Nachr. 170 (1994), 25-37. Zbl0844.46016
  4. [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. Zbl0849.46021
  5. [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. Zbl0315.46037
  6. [6] C. Fefferman and E. M. Stein, H p spaces of several variables, Acta Math. 129 (1972), 137-193. Zbl0257.46078
  7. [7] M. Frazier and B. Jawerth, A discrete transform and decomposition of distribution spaces, J. Funct. Anal. 93 (1990), 34-170. Zbl0716.46031
  8. [8] N. J. H. Heideman, Duality and fractional integration in Lipschitz spaces, Studia Math. 50 (1974), 65-85. Zbl0287.46050
  9. [9] S. Janson and M. H. Taibleson, I teoremi di rappresentazione di Calderón, Rend. Sem. Mat. Univ. Politec. Torino 39 (1981), 27-35. 
  10. [10] V. M. Kokilašvili [V. M. Kokilashvili], Maximal inequalities and multipliers in weighted Triebel-Lizorkin spaces, Soviet Math. Dokl. 19 (1978), 272-276. Zbl0396.46034
  11. [11] J. Peetre, On spaces of Triebel-Lizorkin type, Ark. Mat. 13 (1975), 123-130. Zbl0302.46021
  12. [12] J.-O. Strömberg and A. Torchinsky, Weighted Hardy Spaces, Springer, Berlin, 1989. 
  13. [13] H. Triebel, Theory of Function Spaces, Birkhäuser, Basel, 1983. 
  14. [14] H. Triebel, Characterizations of Besov-Hardy-Sobolev spaces: A unified approach, J. Approx. Theory 52 (1988), 162-203. Zbl0644.46017
  15. [15] H. Triebel, Theory of Function Spaces II, Birkhäuser, Basel, 1992. 

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