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Square functions, bounded analytic semigroups, and applications

100%

Le Merdy C.

Banach Center Publications

2007

tom 75

nr 1

191-220

To any bounded analytic semigroup on Hilbert space or on $L^p$-space, one may associate natural 'square functions'. In this survey paper, we review old and recent results on these square functions, as well as some extensions to various classes of Banach spaces, including noncommutative $L^p$-spaces, Banach lattices, and their subspaces. We give some applications to $H^∞$ functional calculus, similarity problems, multiplier theory, and control theory.

Sums of commuting operators with maximal regularity

63%

Le Merdy C., Simard A.

Studia Mathematica

2001

tom 147

nr 2

103-118

Let Y be a Banach space and let $S ⊂ L_{p}$ be a subspace of an $L_{p}$ space, for some p ∈ (1,∞). We consider two operators B and C acting on S and Y respectively and satisfying the so-called maximal regularity property. Let ℬ and 𝓒 be their natural extensions to $S(Y) ⊂ L_{p}(Y)$. We investigate conditions that imply that ℬ + 𝓒 is closed and has the maximal regularity property. Extending theorems of Lamberton and Weis, we show in particular that this holds if Y is a UMD Banach lattice and $e^{-tB}$ is a positive contraction on $L_{p}$ for any t ≥ 0.

Ograniczanie wyników

1 Banach Center Publications

1 Studia Mathematica

2 Le Merdy C.

1 Simard A.

1 2007

1 2001

Wyniki wyszukiwania

Square functions, bounded analytic semigroups, and applications

Sums of commuting operators with maximal regularity