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Matrix weights via -functions
Author(s):
A.
Volberg
Journal:
J. Amer. Math. Soc.
10
(1997),
445-466.
MSC (1991):
Primary 42B20, 42A50, 47B35
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References:
- [AChS]
- Sh. Axler, S.-Y. A. Chang, and D. Sarason, Products of Toeplitz operators, Integral Equations Operator Theory 1 (1978), 285-309. MR 80d:47039
- [Bl1]
- St. Bloom, A commutator theorem and weighted
, Trans. Amer. Math. Soc. 292 (1985), 103-122. MR 87g:42021 - [Bl2]
- St. Bloom, Applications of commutator theory to weighted
and matrix analogs of , Illinois J. Math. 33 (1989), 464-487. MR 91e:42030 - [BG]
- D.L. Burkholder and R.F. Gundy, Distribution function inequalities for the area integrals, Studia Math. 44 (1972), 527-544. MR 49:5309
- [B1]
- D.L. Burkholder, Explorations in martingale theory and its applications, Ecole d'Ete de Probabilites de Saint-Flour XIX-1989, 1-66, Lecture Notes in Math., 1464, Springer, Berlin, 1991. MR 92m:60037
- [B2]
- D.L. Burkholder, A proof of Pe{\l}czyn\'{s}ki's conjecture for the Haar system, Studia Math. 91 (1988), no. 1, 79-83. MR 89j:46026
- [B3]
- D.L. Burkholder, Boundary value problems and sharp inequalities for martingale transforms, Ann. Probab. 12 (1984), no. 3, 647-702. MR 86b:60080
- [Bu1]
- St. Buckley, Summation conditions on weights, Mich. Math. J. 40 (1993), 153-170. MR 94d:42021
- [Bu2]
- St. Buckley, Estimates for operator norms on weighted spaces and reverse Jensen inequalities, 340 (1993), 253-272. MR 94a:42011
- [FJW]
- M. Frazier, B. Jawerth, and G. Weiss, Littlewood-Paley Theory and the Study of Function Spaces, CBMS Regional Conference Series in Mathematics, 79, 1991, 132 pp. MR 92m:42021
- [FKP]
- R.A. Fefferman, C.E. Kenig, and J. Pipher, The theory of weights and the Dirichlet problem for elliptic equations, Ann. of Math. 134 (1991), 65-124. MR 93h:31010
- [GCRF]
- J. Garcia-Cuerva and J.L. Rubio de Francia, Weighted norm inequalities and related topics, North-Holland, 1985, vii+605 pp. MR 87d:42023
- [Nik]
- N. K. Nikolskii, Treatise on the Shift Operator, Springer-Verlag, NY etc. 1986. MR 87i:47042
- [NT]
- F. Nazarov and S. Treil, The hunt for a Bellman function: applications to estimates of singular integral operators and to other classical problems in harmonic analysis, pp. 1-125, St. Petersburg Math. J. (to appear).
- [S1]
- D. Sarason, Exposed points in
. II, Topics in operator theory: Ernst D. Hellinger memorial volume, 333-347, Oper. Theory Adv. Appl., 48, Birkhauser, Basel, 1990. MR 94a:46031 - [S2]
- D. Sarason, Products of Toeplitz operators, Linear and Complex Analysis Problem Book 3, Part 1, ed. V.P.Havin, N.K.Nikolski, Lecture Notes in Math., 1573, pp. 318-319. MR 96c:00001a
- [Si]
- I.B. Simonenko, Riemann's boundary value problem for
pairs of functions with measurable coefficients and its applications to the study of singular integrals in spaces with weights, Soviet Math. Doklady, 2 (1961), 1391-1394. MR 29:253 - [St]
- E. Stein, Harmonic analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Univ. Press, Princeton, NJ, 1993. xiii+695 pp. MR 95c:42002
- [Str]
- D.W. Stroock, Probability Theory, an Analytic View, Cambridge Univ. Press, Cambridge, 1993. xvi+512 pp. MR 95f:6000
- [TV1]
- S. Treil and A. Volberg, Wavelets and the angle between past and future, J. Funct. Anal. 143 (1997) (to appear).
- [TV2]
- S. Treil and A. Volberg, Continuous wavelet decomposition and a vector Hunt-Muckenhoupt-Wheeden Theorem, Preprint, pp. 1-16, 1995; Ark. fur Mat. (to appear).
- [TV3]
- S. Treil and A. Volberg, Completely regular multivariate processes and matrix weighted estimates, Preprint, pp.1-15, 1996.
- [TVZ]
- S. Treil, A. Volberg, and D. Zheng, Hilbert transform, Toeplitz operators and Hankel operators, and invariant
weights, Revista Mat. Iberoamericana (to appear).
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Additional Information:
A.
Volberg
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
Email:
volberg@math.msu.edu
DOI:
10.1090/S0894-0347-97-00233-6
PII:
S 0894-0347(97)00233-6
Keywords:
$A_{p}$ weights,
matrix-functions,
area integrals,
singular integrals,
Carleson measures,
Triebel-Lizorkin spaces
Received by editor(s):
May 24, 1996
Received by editor(s) in revised form:
December 2, 1996
Additional Notes:
This work was partially supported by National Science Foundation Grant DMS9622936
Copyright of article:
Copyright
1997,
American Mathematical Society
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