Currently displaying 1 – 9 of 9

Showing per page

Order by Relevance | Title | Year of publication

Duality on vector-valued weighted harmonic Bergman spaces

Salvador Pérez-Esteva — 1996

Studia Mathematica

We study the duals of the spaces A p α ( X ) of harmonic functions in the unit ball of n with values in a Banach space X, belonging to the Bochner L p space with weight ( 1 - | x | ) α , denoted by L p α ( X ) . For 0 < α < p-1 we construct continuous projections onto A p α ( X ) providing a decomposition L p α ( X ) = A p α ( X ) + M p α ( X ) . We discuss the conditions on p, α and X for which A p α ( X ) * = A q α ( X * ) and M p α ( X ) * = M q α ( X * ) , 1/p+1/q = 1. The last equality is equivalent to the Radon-Nikodým property of X*.

On Bell's duality theorem for harmonic functions

Joaquín MotosSalvador Pérez-Esteva — 1999

Studia Mathematica

Define h ( E ) as the subspace of C ( B ̅ L , E ) consisting of all harmonic functions in B, where B is the ball in the n-dimensional Euclidean space and E is any Banach space. Consider also the space h - ( E * ) consisting of all harmonic E*-valued functions g such that ( 1 - | x | ) m f is bounded for some m>0. Then the dual h ( E * ) is represented by h - ( E * ) through f , g 0 = l i m r 1 ʃ B f ( r x ) , g ( x ) d x , f h - ( E * ) , g h ( E ) . This extends the results of S. Bell in the scalar case.

Page 1

Download Results (CSV)