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Failure of Nehari's theorem for multiplicative Hankel forms in Schatten classes

100%

Brevig O., Perfekt K.-M.

Studia Mathematica

2015

tom 228

nr 2

101-108

Ortega-Cerdà-Seip demonstrated that there are bounded multiplicative Hankel forms which do not arise from bounded symbols. On the other hand, when such a form is in the Hilbert-Schmidt class 𝓢₂, Helson showed that it has a bounded symbol. The present work investigates forms belonging to the Schatten classes between these two cases. It is shown that for every $p > (1- log π/log 4)^{-1}$ there exist multiplicative Hankel forms in the Schatten class $𝓢_{p}$ which lack bounded symbols. The lower bound on p is in a certain sense optimal when the symbol of the multiplicative Hankel form is a product of homogeneous linear polynomials.

Some Hilbert spaces related with the Dirichlet space

71%

Arcozzi N., Mozolyako P., Perfekt K.-M., Richter S., Sarfatti G.

Concrete Operators

2016

tom 3

nr 1

94-101

We study the reproducing kernel Hilbert space with kernel kd , where d is a positive integer and k is the reproducing kernel of the analytic Dirichlet space.

Ograniczanie wyników

1 Concrete Operators

1 Studia Mathematica

2 Perfekt K.-M.

1 Arcozzi N.

1 Brevig O.

1 Mozolyako P.

1 Richter S.

1 Sarfatti G.

1 2016

1 2015

Wyniki wyszukiwania

Failure of Nehari's theorem for multiplicative Hankel forms in Schatten classes

Some Hilbert spaces related with the Dirichlet space