Currently displaying 1 – 1 of 1

Showing per page

Order by Relevance | Title | Year of publication

A Hankel matrix acting on Hardy and Bergman spaces

Petros GalanopoulosJosé Ángel Peláez — 2010

Studia Mathematica

Let μ be a finite positive Borel measure on [0,1). Let μ = ( μ n , k ) n , k 0 be the Hankel matrix with entries μ n , k = [ 0 , 1 ) t n + k d μ ( t ) . The matrix μ induces formally an operator on the space of all analytic functions in the unit disc by the fomula μ ( f ) ( z ) = n = 0 i ( k = 0 μ n , k a k ) z , z ∈ , where f ( z ) = n = 0 a z is an analytic function in . We characterize those positive Borel measures on [0,1) such that μ ( f ) ( z ) = [ 0 , 1 ) f ( t ) / ( 1 - t z ) d μ ( t ) for all f in the Hardy space H¹, and among them we describe those for which μ is bounded and compact on H¹. We also study the analogous problem for the Bergman space A².

Page 1

Download Results (CSV)