Extension of a result of Benedek, Calderón and Panzone

Benedek, A., Calderón, A. andPanzone, R., Convolution operators on Banach space valued functions,Proc. Nat. Acad. Sci. U.S.A.,48 (1962), 356–365.

Bourgain, J., Some remarks on Banach spaces in which martingale difference sequences are unconditional,Ark. Mat.,22 (1984).

Burkholder, D., A geometrical characterization of Banach spaces in which martingale difference sequences are unconditional,Ann. Probab.,9 (1981), 997–1011.

Burkholder D., A geometrical condition that implies the existence of certain singular integrals of Banach-space-valued functions,Proc. Conf. Harmonic Analysis in Honor of Antony Zygmund, Chicago, 1982, Wadsworth, Belmont, 1983.

Coifman, R. R. andFefferman, C., Weight norm inequalities for maximal functions and singular integrals,Studia Math.,51, (1974), 241–250.

Cordoba, A. andFefferman, C., A weighted norm inequality for singular integrals,Studia Math.,57, (1976), 97–101.

Garnett, J. B.,Bounded analytic functions, Academic Press, 1971.

Garsia, A.,Martingale Inequalities, Seminar Notes on Recent Progress, Mathematics lecture note series, W. A. Benjamin, Reading, Massachusetts, 1973.

Gundy, R. F. andWheeden, R. L., Weighted integral inequalities for the nontangential maximal function, Lusin area integral and Walsh-Paley series,Studia Math.,49, (1974), 107–124.

Lindenstrauss, J. andTzafriri, L.,Classical Banach Spaces, Vol. II, Ergebnisse der Mathematik97, Springer-Verlag, Berlin, Heidelberg, New York, 1970.

Muckenhoupt, B., The equivalence of two conditions for weight functions,Studia Math. 49, (1974), 101–106.