Matrix weights via functions
Author:
A. Volberg
Journal:
J. Amer. Math. Soc. 10 (1997), 445466
MSC (1991):
Primary 42B20, 42A50, 47B35
MathSciNet review:
1423034
Fulltext PDF Free Access
References 
Similar Articles 
Additional Information
 [AChS]
Sheldon
Axler, SunYung
A. Chang, and Donald
Sarason, Products of Toeplitz operators, Integral Equations
Operator Theory 1 (1978), no. 3, 285–309. MR 511973
(80d:47039), http://dx.doi.org/10.1007/BF01682841
 [Bl1]
Steven
Bloom, A commutator theorem and weighted
BMO, Trans. Amer. Math. Soc.
292 (1985), no. 1,
103–122. MR
805955 (87g:42021), http://dx.doi.org/10.1090/S00029947198508059555
 [Bl2]
Steven
Bloom, Applications of commutator theory to weighted BMO and matrix
analogs of 𝐴₂, Illinois J. Math. 33
(1989), no. 3, 464–487. MR 996354
(91e:42030)
 [BG]
D.
L. Burkholder and R.
F. Gundy, Distribution function inequalities for the area
integral, Studia Math. 44 (1972), 527–544.
Collection of articles honoring the completion by Antoni Zygmund of 50
years of scientific activity, VI. MR 0340557
(49 #5309)
 [B1]
Donald
L. Burkholder, Explorations in martingale theory and its
applications, École d’Été de
Probabilités de SaintFlour XIX—1989, Lecture Notes in Math.,
vol. 1464, Springer, Berlin, 1991, pp. 1–66. MR 1108183
(92m:60037), http://dx.doi.org/10.1007/BFb0085167
 [B2]
Donald
L. Burkholder, A proof of Pełczynśki’s
conjecture for the Haar system, Studia Math. 91
(1988), no. 1, 79–83. MR 957287
(89j:46026)
 [B3]
D.
L. Burkholder, Boundary value problems and sharp inequalities for
martingale transforms, Ann. Probab. 12 (1984),
no. 3, 647–702. MR 744226
(86b:60080)
 [Bu1]
Stephen
M. Buckley, Summation conditions on weights, Michigan Math. J.
40 (1993), no. 1, 153–170. MR 1214060
(94d:42021), http://dx.doi.org/10.1307/mmj/1029004679
 [Bu2]
Stephen
M. Buckley, Estimates for operator norms on
weighted spaces and reverse Jensen inequalities, Trans. Amer. Math. Soc. 340 (1993), no. 1, 253–272. MR 1124164
(94a:42011), http://dx.doi.org/10.1090/S00029947199311241640
 [FJW]
Michael
Frazier, Björn
Jawerth, and Guido
Weiss, LittlewoodPaley theory and the study of function
spaces, CBMS Regional Conference Series in Mathematics, vol. 79,
Published for the Conference Board of the Mathematical Sciences,
Washington, DC; by the American Mathematical Society, Providence, RI, 1991.
MR
1107300 (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. (2) 134 (1991),
no. 1, 65–124. MR 1114608
(93h:31010), http://dx.doi.org/10.2307/2944333
 [GCRF]
José
GarcíaCuerva and José
L. Rubio de Francia, Weighted norm inequalities and related
topics, NorthHolland Mathematics Studies, vol. 116,
NorthHolland Publishing Co., Amsterdam, 1985. Notas de Matemática
[Mathematical Notes], 104. MR 807149
(87d:42023)
 [Nik]
N.
K. Nikol′skiĭ, Treatise on the shift operator,
Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of
Mathematical Sciences], vol. 273, SpringerVerlag, Berlin, 1986.
Spectral function theory; With an appendix by S. V. Hruščev
[S. V. Khrushchëv] and V. V. Peller; Translated from the Russian by
Jaak Peetre. MR
827223 (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. 1125, St. Petersburg Math. J. (to appear).
 [S1]
Donald
Sarason, Exposed points in 𝐻¹. II, Topics in
operator theory: Ernst D. Hellinger memorial volume, Oper. Theory Adv.
Appl., vol. 48, Birkhäuser, Basel, 1990, pp. 333–347.
MR
1207406 (94a:46031)
 [S2]
V.
P. Havin and N.
K. Nikolski (eds.), Linear and complex analysis. Problem book 3.
Part I, Lecture Notes in Mathematics, vol. 1573, SpringerVerlag,
Berlin, 1994. MR
1334345 (96c:00001a)
 [Si]
I.
B. Simonenko, The Riemann boundaryvalue problem for 𝑛
pairs of functions with measurable coefficients and its application to the
study of singular integrals in 𝐿_{𝑝} spaces with
weights, Izv. Akad. Nauk SSSR Ser. Mat. 28 (1964),
277–306 (Russian). MR 0162949
(29 #253)
 [St]
Elias
M. Stein, Harmonic analysis: realvariable methods, orthogonality,
and oscillatory integrals, Princeton Mathematical Series,
vol. 43, Princeton University Press, Princeton, NJ, 1993. With the
assistance of Timothy S. Murphy; Monographs in Harmonic Analysis, III. MR 1232192
(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 HuntMuckenhouptWheeden Theorem, Preprint, pp. 116, 1995; Ark. fur Mat. (to appear).
 [TV3]
S. Treil and A. Volberg, Completely regular multivariate processes and matrix weighted estimates, Preprint, pp.115, 1996.
 [TVZ]
S. Treil, A. Volberg, and D. Zheng, Hilbert transform, Toeplitz operators and Hankel operators, and invariant weights, Revista Mat. Iberoamericana (to appear).
 [AChS]
 Sh. Axler, S.Y. A. Chang, and D. Sarason, Products of Toeplitz operators, Integral Equations Operator Theory 1 (1978), 285309. MR 80d:47039
 [Bl1]
 St. Bloom, A commutator theorem and weighted , Trans. Amer. Math. Soc. 292 (1985), 103122. MR 87g:42021
 [Bl2]
 St. Bloom, Applications of commutator theory to weighted and matrix analogs of , Illinois J. Math. 33 (1989), 464487. MR 91e:42030
 [BG]
 D.L. Burkholder and R.F. Gundy, Distribution function inequalities for the area integrals, Studia Math. 44 (1972), 527544. MR 49:5309
 [B1]
 D.L. Burkholder, Explorations in martingale theory and its applications, Ecole d'Ete de Probabilites de SaintFlour XIX1989, 166, 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, 7983. MR 89j:46026
 [B3]
 D.L. Burkholder, Boundary value problems and sharp inequalities for martingale transforms, Ann. Probab. 12 (1984), no. 3, 647702. MR 86b:60080
 [Bu1]
 St. Buckley, Summation conditions on weights, Mich. Math. J. 40 (1993), 153170. MR 94d:42021
 [Bu2]
 St. Buckley, Estimates for operator norms on weighted spaces and reverse Jensen inequalities, 340 (1993), 253272. MR 94a:42011
 [FJW]
 M. Frazier, B. Jawerth, and G. Weiss, LittlewoodPaley 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), 65124. MR 93h:31010
 [GCRF]
 J. GarciaCuerva and J.L. Rubio de Francia, Weighted norm inequalities and related topics, NorthHolland, 1985, vii+605 pp. MR 87d:42023
 [Nik]
 N. K. Nikolskii, Treatise on the Shift Operator, SpringerVerlag, 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. 1125, St. Petersburg Math. J. (to appear).
 [S1]
 D. Sarason, Exposed points in . II, Topics in operator theory: Ernst D. Hellinger memorial volume, 333347, 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. 318319. 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), 13911394. MR 29:253
 [St]
 E. Stein, Harmonic analysis: RealVariable 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 HuntMuckenhouptWheeden Theorem, Preprint, pp. 116, 1995; Ark. fur Mat. (to appear).
 [TV3]
 S. Treil and A. Volberg, Completely regular multivariate processes and matrix weighted estimates, Preprint, pp.115, 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:
http://dx.doi.org/10.1090/S0894034797002336
PII:
S 08940347(97)002336
Keywords:
$A_{p}$ weights,
matrixfunctions,
area integrals,
singular integrals,
Carleson measures,
TriebelLizorkin 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
Article copyright:
© Copyright 1997
American Mathematical Society
