## 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.Â 3, 285â309. MR**511973**, DOI 10.1007/BF01682841 - Steven Bloom,
*A commutator theorem and weighted BMO*, Trans. Amer. Math. Soc.**292**(1985), no.Â 1, 103â122. 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.Â 3, 464â487. MR**996354** - D. L. Burkholder and R. F. Gundy,
*Distribution function inequalities for the area integral*, Studia Math.**44**(1972), 527â544. MR**340557**, DOI 10.4064/sm-44-6-527-544 - Donald L. Burkholder,
*Explorations in martingale theory and its applications*, Ăcole dâĂtĂ© de ProbabilitĂ©s de Saint-Flour XIXâ1989, Lecture Notes in Math., vol. 1464, Springer, Berlin, 1991, pp.Â 1â66. MR**1108183**, DOI 10.1007/BFb0085167 - Donald L. Burkholder,
*A proof of PeĆczynĆkiâs conjecture for the Haar system*, Studia Math.**91**(1988), no.Â 1, 79â83. 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.Â 3, 647â702. MR**744226** - Stephen M. Buckley,
*Summation conditions on weights*, Michigan Math. J.**40**(1993), no.Â 1, 153â170. 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.Â 1, 253â272. MR**1124164**, DOI 10.1090/S0002-9947-1993-1124164-0 - Michael Frazier, BjĂ¶rn 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.Â 1, 65â124. MR**1114608**, DOI 10.2307/2944333 - JosĂ© GarcĂa-Cuerva and JosĂ© L. Rubio de Francia,
*Weighted norm inequalities and related topics*, North-Holland Mathematics Studies, vol. 116, North-Holland Publishing Co., Amsterdam, 1985. Notas de MatemĂĄtica [Mathematical Notes], 104. MR**807149** - N. K. NikolâČskiÄ,
*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. HruĆĄÄev [S. V. KhrushchĂ«v] 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, BirkhĂ€user, Basel, 1990, pp.Â 333â347. 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), 277â306 (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), 63â97. 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).

## Bibliographic Information

**A. Volberg**- Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
- Email: volberg@math.msu.edu
- 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 1997 American Mathematical Society
- Journal: J. Amer. Math. Soc.
**10**(1997), 445-466 - MSC (1991): Primary 42B20, 42A50, 47B35
- DOI: https://doi.org/10.1090/S0894-0347-97-00233-6
- MathSciNet review: 1423034