56 research outputs found
Linear functions and duality on the infinite polytorus
We consider the following question: Are there exponents such that the
Riesz projection is bounded from to on the infinite polytorus? We
are unable to answer the question, but our counter-example improves a result of
Marzo and Seip by demonstrating that the Riesz projection is unbounded from
to if . A similar result can be extracted for
any . Our approach is based on duality arguments and a detailed study of
linear functions. Some related results are also presented.Comment: This paper has been accepted for publication in Collectanea
Mathematic
Sharp norm estimates for composition operators and Hilbert-type inequalities
Let denote the Hardy space of Dirichlet series with square summable coefficients and suppose that
is a symbol generating a composition operator on by
. Let denote the Riemann zeta
function and the unique positive solution of the equation
. We obtain sharp upper bounds for the norm of
on when
, by relating such sharp
upper bounds to the best constant in a family of discrete Hilbert-type
inequalities.Comment: This paper has been accepted for publication in Bulletin of the LM
High pseudomoments of the Riemann zeta function
The pseudomoments of the Riemann zeta function, denoted ,
are defined as the th integral moments of the th partial sum of
on the critical line. We improve the upper and lower bounds for the
constants in the estimate as
for fixed , thereby determining the two first terms of the
asymptotic expansion. We also investigate uniform ranges of where this
improved estimate holds and when may be lower bounded by the
th power of the norm of the th partial sum of on
the critical line.Comment: This paper has been accepted for publication in Journal of Number
Theor
Minimal norm Hankel operators
Let be a function in the Hardy space . The
associated (small) Hankel operator is said to have minimal
norm if the general lower norm bound is attained. Minimal norm Hankel operators are
natural extremal candidates for the Nehari problem. If , then
has minimal norm if and only if is a constant
multiple of an inner function. Constant multiples of inner functions generate
minimal norm Hankel operators also when , but in this case there are
other possibilities as well. We investigate two different classes of symbols
generating minimal norm Hankel operators and obtain two different refinements
of a counter-example due to Ortega-Cerd\`{a} and Seip
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