Inequalities for square functions induced by operators on a Hilbert space
Abstract
Let U:H→H be a unitary operator on a Hilbert space H and for all . Suppsoe that (nk) is a lacunary sequence with no non-trivial common divisor, then there exists a positive constant C such thatLet T be a contraction on a Hilbert space H and letfor all . Suppose that (nk) is a lacunary sequence with no non-trivial common divisor, then there exist a Hilbert space K containing H as a closed subspace, and an ortogonal projection P:K→H such that Mathematics Subject Classification: 47A63.
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- An Oscillation Inequality on a Complex Hilbert Space ↗
S. Demir · Russian Mathematics · 2024
Let $$T$$ be a contraction on a complex Hilbert space $$\mathcal{H}$$ , and for $$f \in \mathcal{H}$$ define $${{A}_{n}}(T)f = \frac{1}{n}\sum\limits_{j = 1}^n \,{{T}^{j}}f.$$ Let $$({{n}_{k}})$$ be an increasing sequence and $$M$$ be any sequence. We prove that there exists a positive constant $$C$$ such that $${{\left( {\sum\limits_{k = 1}^\infty \mathop {\sup }\limits_{\substack{ {{n}_{k}} \leqslant m < {{n}_{{k + 1}}}…
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