A weak molecule condition for certain Triebel-Lizorkin spaces
Studia Mathematica (1992)
- Volume: 101, Issue: 2, page 113-122
- ISSN: 0039-3223
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topHofmann, Steve. "A weak molecule condition for certain Triebel-Lizorkin spaces." Studia Mathematica 101.2 (1992): 113-122. <http://eudml.org/doc/215895>.
@article{Hofmann1992,
abstract = {A weak molecule condition is given for the Triebel-Lizorkin spaces Ḟ\_p^\{α,q\}, with 0 < α < 1 and 1 < p, q < ∞. As an easy corollary, one may deduce, by atomic-molecular methods, a Triebel-Lizorkin space "T1" Theorem of Han and Sawyer, and Han, Jawerth, Taibleson and Weiss, for Calderón-Zygmund kernels K(x,y) which are not assumed to satisfy any regularity condition in the y variable.},
author = {Hofmann, Steve},
journal = {Studia Mathematica},
keywords = {weak molecule condition; Triebel-Lizorkin spaces; atomic-molecular methods},
language = {eng},
number = {2},
pages = {113-122},
title = {A weak molecule condition for certain Triebel-Lizorkin spaces},
url = {http://eudml.org/doc/215895},
volume = {101},
year = {1992},
}
TY - JOUR
AU - Hofmann, Steve
TI - A weak molecule condition for certain Triebel-Lizorkin spaces
JO - Studia Mathematica
PY - 1992
VL - 101
IS - 2
SP - 113
EP - 122
AB - A weak molecule condition is given for the Triebel-Lizorkin spaces Ḟ_p^{α,q}, with 0 < α < 1 and 1 < p, q < ∞. As an easy corollary, one may deduce, by atomic-molecular methods, a Triebel-Lizorkin space "T1" Theorem of Han and Sawyer, and Han, Jawerth, Taibleson and Weiss, for Calderón-Zygmund kernels K(x,y) which are not assumed to satisfy any regularity condition in the y variable.
LA - eng
KW - weak molecule condition; Triebel-Lizorkin spaces; atomic-molecular methods
UR - http://eudml.org/doc/215895
ER -
References
top- [CZ] A. P. Calderón and A. Zygmund, On the existence of certain singular integrals, Acta Math. 88 (1952), 85-139. Zbl0047.10201
- [CDMS] R. Coifman, G. David, Y. Meyer and S. Semmes, ω-Calderón-Zygmund operators, in: Proc. Conf. Harmonic Analysis and PDE, El Escorial 1987, Lecture Notes in Math. 1384, Springer, Berlin 1989, 132-145.
- [DJS] G. David, J.-L. Journé and S. Semmes, Calderón-Zygmund operators, para-accretive functions and interpolation, preprint. Zbl0604.42014
- [FHJW] M. Frazier, Y. S. Han, B. Jawerth and G. Weiss, The T1 Theorem for Triebel-Lizorkin spaces, in: Proc. Conf. Harmonic Analysis and PDE, El Escorial 1987, Lecture Notes in Math. 1384, Springer, Berlin 1989, 168-181. Zbl0679.46026
- [FJ] M. Frazier and B. Jawerth, The φ-transform and applications to distribution spaces, in: Function Spaces and Applications, M. Cwikel et al. (eds.), Lecture Notes in Math. 1302, Springer, Berlin 1988, 223-246.
- [HH] Y. S. Han and S. Hofmann, T1 Theorems for Besov and Triebel-Lizorkin spaces, Trans. Amer. Math. Soc., to appear. Zbl0779.42010
- [HJTW] Y. S. Han, B. Jawerth, M. Taibleson and G. Weiss, Littlewood-Paley theory and ϵ-families of operators, Colloq. Math. 60/61 (1990), 321-359. Zbl0763.46024
- [HS] Y. S. Han and E. T. Sawyer, Para-accretive functions, the weak boundedness property and the Tb Theorem, Rev. Mat. Iberoamericana 6 (1990), 17-41. Zbl0723.42005
- [L] P. G. Lemarié, Continuité sur les espaces de Besov des opérateurs définis par des intégrales singulières, Ann. Inst. Fourier (Grenoble) 35 (4) (1985), 175-187. Zbl0555.47032
- [M] Y. Meyer, Les nouveaux opérateurs de Calderón-Zygmund, in: Colloque en l'honneur de L. Schwartz, Astérisque 131 (1985), 237-254.
- [MM] M. Meyer, Continuité Besov de certains opérateurs intégraux singuliers, thèse de 3e cycle, Orsay 1985.
- [T] R. Torres, Boundedness results for operators with singular kernels on distribution spaces, Mem. Amer. Math. Soc. 442 (1991). Zbl0737.47041
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