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[ACS]Axler, S., Chang, S.-Y. A. andSarason, D., Products of Toeplitz operators,Integral Equations Operator Theory 1 (1978), 285–309.
[B1]Bloom, S., A commutator theorem and weighted BMO,Trans. Amer. Math. Soc. 292 (1985), 103–122.
[B2]Bloom, S., Applications of commutator theory to weighted BMO and matrix analogs ofA 2,Illinois J. Math. 33 (1989), 464–487.
[D]Daubechies, I.,Ten Lectures on Wavelets, CBMS-NSF Regional Conf. Ser. in Appl. Math.61, Soc. Ind. Appl. Math., Philadelphia, Pa., 1992.
[Do]Douglas, R. G., On majorization, factorization, and range inclusion of operators on Hilbert space,Proc. Amer. Math. Soc. 17 (1966), 413–415.
[GCRF]García-Cuerva, J. andRubio de Francia, J. L.,Weighted Norm Inequalities and Related Topics, North-Holland, Amsterdam-New York, 1985.
[G]Garnett, J. B.,Bounded Analytic Functions, Academic Press, Orlando, Fla., 1981.
[HS]Helson, H. andSarason, D., Past and future,Math. Scand.,21 (1967), 5–16.
[HMW]Hunt, R. A., Muckenhoupt, B. andWheeden, R. L., Weighted norm inequalities for the conjugate function and the Hilbert transform,Trans. Amer. Math. Soc. 176 (1973), 227–251.
[KS]Kolmogorov, A. andSeliverstov, G., Sur la convergence de series de Fourier,C. R. Acad. Sci. Paris 178 (1925), 303–305.
[NT]Nazarov, F. andTreil, S., The hunt for a Bellman function: applications to estimates of singular integral operators and to other classical problems in harmonic analysis,Algebra i Analiz 8:5 (1996), 32–162.
[N]Nikolskii, N. K.,Treatise on the Shift Operator, Springer-Verlag, Berlin-New York, 1986.
[R]Rozanov, Yu. A.,Stationary Stochastic Processes, Holden-Day, San Francisco, Calif., 1967.
[S1]Sarason, D., Exposed points inH 1. II, inTopics in Operator Theory: Ernst D. Hellinger Memorial Volume (de Branges, L., Gohberg, I. and Rovnyak, J., eds.), Oper. Theory Adv. Appl.48, pp. 333–347, Birkhäuser, Basel, 1990.
[S2]Sarason, D., Products of Toeplitz operators, inLinear and Complex Analysis Problem Book 3, Part I (Havin, V. P. and Nikolski, N. K., eds.). Lecture Notes in Math.1573, pp. 318–319, Springer-Verlag, Berlin-Heidelberg, 1994.
[Si]Simonenko, I. B., Riemann's boundary value problem forn pairs of functions with measurable coefficients and its applications to the study of singular integrals inL p spaces with weights,Dokl Akad. Nauk SSSR 141 (1961), 36–39 (Russian). English transl.:Soviet Math. Dokl. 2 (1961), 1391–1394.
[St]Stein, E.,Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Univ. Press, Princeton, N. J., 1993.
[T]Treil, S., Geometric methods in spectral theory of vector valued functions: Some recent results, inToeplitz Operators and Spectral Function Theory (Nikolskii, N. K., ed.), Oper. Theory Adv. Appl.42, pp. 209–280, Birkhäuser, Basel, 1989.
[TV1]Treil, S. andVolberg, A., Wavelets and the angle between past and future,J. Funct. Anal. 143 (1997), 269–308.
[TV2]Treil, S. andVolberg, A., A simple proof of Hunt-Muckenhoupt-Wheeden theorem,Preprint, 1995.
[TV3]Treil, S. andVolberg, A., Completely regular multivariate processes and matrix weighted estimates,Preprint, 1996.
[TVZ]Treil, S. Volberg, A. andZheng, D., Hilbert transform, Toeplitz operators and Hankel operators, and invariant A∞ weights, to appear inRev. Mat. Iberoamericana.
[V]Volberg, A., MatrixA p weights viaS-functions, to appear inJ. Amer. Math. Soc.
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Treil, S., Volberg, A. Continuous frame decomposition and a vector Hunt-Muckenhoupt-Wheeden theorem. Ark. Mat. 35, 363–386 (1997). https://doi.org/10.1007/BF02559975
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DOI: https://doi.org/10.1007/BF02559975