Matrix 𝐴_{𝑝} weights via 𝑆-functions

Volberg, A.

doi:10.1090/S0894-0347-97-00233-6

Matrix $A_p$ weights via $S$-functions
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by A. Volberg

J. Amer. Math. Soc. 10 (1997), 445-466

DOI: https://doi.org/10.1090/S0894-0347-97-00233-6

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References

Sheldon Axler, Sun-Yung A. Chang, and Donald Sarason, Products of Toeplitz operators, Integral Equations Operator Theory 1 (1978), no. 3, 285–309. MR 511973, DOI 10.1007/BF01682841
Steven Bloom, A commutator theorem and weighted BMO, Trans. Amer. Math. Soc. 292 (1985), no. 1, 103–122. MR 805955, DOI 10.1090/S0002-9947-1985-0805955-5
Steven Bloom, Applications of commutator theory to weighted BMO and matrix analogs of $A_2$, Illinois J. Math. 33 (1989), no. 3, 464–487. MR 996354
D. L. Burkholder and R. F. Gundy, Distribution function inequalities for the area integral, Studia Math. 44 (1972), 527–544. MR 340557, DOI 10.4064/sm-44-6-527-544
Donald L. Burkholder, Explorations in martingale theory and its applications, École d’Été de Probabilités de Saint-Flour XIX—1989, Lecture Notes in Math., vol. 1464, Springer, Berlin, 1991, pp. 1–66. MR 1108183, DOI 10.1007/BFb0085167
Donald L. Burkholder, A proof of Pełczynśki’s conjecture for the Haar system, Studia Math. 91 (1988), no. 1, 79–83. MR 957287, DOI 10.4064/sm-91-1-79-83
D. L. Burkholder, Boundary value problems and sharp inequalities for martingale transforms, Ann. Probab. 12 (1984), no. 3, 647–702. MR 744226
Stephen M. Buckley, Summation conditions on weights, Michigan Math. J. 40 (1993), no. 1, 153–170. MR 1214060, DOI 10.1307/mmj/1029004679
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, DOI 10.1090/S0002-9947-1993-1124164-0
Michael Frazier, Björn Jawerth, and Guido Weiss, Littlewood-Paley 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, DOI 10.1090/cbms/079
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, DOI 10.2307/2944333
José García-Cuerva and José L. Rubio de Francia, Weighted norm inequalities and related topics, North-Holland Mathematics Studies, vol. 116, North-Holland Publishing Co., Amsterdam, 1985. Notas de Matemática [Mathematical Notes], 104. MR 807149
N. K. Nikol′skiĭ, Treatise on the shift operator, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 273, Springer-Verlag, 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, DOI 10.1007/978-3-642-70151-1
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).
Donald Sarason, Exposed points in $H^1$. II, Topics in operator theory: Ernst D. Hellinger memorial volume, Oper. Theory Adv. Appl., vol. 48, Birkhäuser, Basel, 1990, pp. 333–347. MR 1207406
V. P. Havin and N. K. Nikolski (eds.), Linear and complex analysis. Problem book 3. Part I, Lecture Notes in Mathematics, vol. 1573, Springer-Verlag, Berlin, 1994. MR 1334345
I. B. Simonenko, The Riemann boundary-value 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
Elias M. Stein, Harmonic analysis: real-variable 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
L. Kantorovitch, The method of successive approximations for functional equations, Acta Math. 71 (1939), 63–97. MR 95, DOI 10.1007/BF02547750
S. Treil and A. Volberg, Wavelets and the angle between past and future, J. Funct. Anal. 143 (1997) (to appear).
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).
S. Treil and A. Volberg, Completely regular multivariate processes and matrix weighted estimates, Preprint, pp.1-15, 1996.
S. Treil, A. Volberg, and D. Zheng, Hilbert transform, Toeplitz operators and Hankel operators, and invariant $A_{\infty }$ weights, Revista Mat. Iberoamericana (to appear).