We introduce and study the class of mean2-bounded operators on Hilbert space. These operators, which are characterized by a uniform boundedness condition on the ''quadratic averages'' of their powers, are intimately related to operator-valued weight sequences and weighted norm inequalities. Mean2-bounded operators exhibit a lively interplay with the discrete Hilbert transform in an array of settings. Under appropriate circumstances, mean2-bounded operators have a rich spectral theory leading to powerful transference properties.
Positivity – Springer Journals
Published: Sep 28, 2004
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