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Vector valued inequalities for strongly singular Calderón-Zygmund operators.

Josefina Alvarez, Mario Milman (1986)

Revista Matemática Iberoamericana

In this article we consider a theory of vector valued strongly singular operators. Our results include Lp, Hp and BMO continuity results. Moreover, as is well known, vector valued estimates are closely related to weighted norm inequalities. These results are developed in the first four sections of our paper. In section 5 we use our vector valued singular integrals to estimate the corresponding maximal operators. Finally in section 6 we discuss applications to weighted norm inequalities for pseudo-differential...

Weak-star point of continuity property and Schauder bases

Ginés López-Pérez, José A. Soler-Arias (2013)

Studia Mathematica

We characterize the weak-star point of continuity property for subspaces of dual spaces with separable predual and we deduce that the weak-star point of continuity property is determined by subspaces with a Schauder basis in the natural setting of dual spaces of separable Banach spaces. As a consequence of the above characterization we show that a dual space has the Radon-Nikodym property if, and only if, every seminormalized topologically weak-star null tree has a boundedly complete branch, which...

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