Displaying similar documents to “On extrapolation blowups in the l p scale.”

The commutators of analysis and interpolation

Cerdà, Joan

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The boundedness properties of commutators for operators are of central importance in Mathematical Analysis, and some of these commutators arise in a natural way from interpolation theory. Our aim is to present a general abstract method to prove the boundedness of the commutator [ T , Ω ] for linear operators T and certain unbounded operators Ω that appear in interpolation theory, previously known and a priori unrelated for both real and complex interpolation methods, and also to show how the...

Approach regions for the square root of the Poisson kernel and boundary functions in certain Orlicz spaces

M. Brundin (2007)

Czechoslovak Mathematical Journal

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If the Poisson integral of the unit disc is replaced by its square root, it is known that normalized Poisson integrals of L p and weak L p boundary functions converge along approach regions wider than the ordinary nontangential cones, as proved by Rönning and the author, respectively. In this paper we characterize the approach regions for boundary functions in two general classes of Orlicz spaces. The first of these classes contains spaces L Φ having the property L L Φ L p , 1 p < . The second contains...