On square functions associated to sectorial operators

Merdy, Christian Le

doi:10.24033/bsmf.2462

Cited by 44 publications

(48 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For simplicity we will prove (2) only. The proof of (1) is quite similar (see [43], [1], or [35] for details). Let θ ∈ (ω, π), and let F and G be two nonzero functions belonging to…”

Section: Dmentioning

confidence: 65%

“…See [35] for details. We do not know if this result remains true without assuming that A is R-sectorial.…”

Section: Theorem 51 ([35]mentioning

confidence: 99%

“…We also include a subsection on Rademacher boundedness, a recent notion which now plays a key 192 C. LE MERDY role in the development of the subject (see e.g. [29,30,35,56,57]). Section 3 is devoted to square functions on Hilbert space.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Square functions, bounded analytic semigroups, and applications

Merdy

2007

Perspectives in Operator Theory

Self Cite

View full text Add to dashboard Cite

Abstract. 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. The purpose of this survey paper is to give a review of the various connections between functional calculus and square functions, as well as some of their applications to several aspects of the theory of semigroups. Of course it is only a selection of these applications, obviously influenced by the author's tastes.In Section 2, we briefly review all necessary definitions and basic results concerning sectorial operators, H ∞ functional calculus, and bounded analytic semigroups. We also include a subsection on Rademacher boundedness, a recent notion which now plays a key

show abstract

“…For simplicity we will prove (2) only. The proof of (1) is quite similar (see [43], [1], or [35] for details). Let θ ∈ (ω, π), and let F and G be two nonzero functions belonging to…”

Section: Dmentioning

confidence: 65%

“…See [35] for details. We do not know if this result remains true without assuming that A is R-sectorial.…”

Section: Theorem 51 ([35]mentioning

confidence: 99%

See 1 more Smart Citation

Square functions, bounded analytic semigroups, and applications

Merdy

2007

Perspectives in Operator Theory

Self Cite

View full text Add to dashboard Cite

show abstract

“…For q = 2, this is a consequence of the Gaussian estimates for the kernels of e −tH , t > 0 (this was first proved in [2] using the vector-valued version of the work in [11]. See [1] for a more general argument in this spirit or [26] for an abstract proof relying on functional calculus).…”

Section: Tome 57 (2007) Fasciculementioning

confidence: 99%

Maximal inequalities and Riesz transform estimates on L^p spaces for Schrödinger operators with nonnegative potentials

Auscher¹,

Ali²

2007

Ann. inst. Fourier

142

View full text Add to dashboard Cite

show abstract

“…X = C) has benefited from this probabilistic point of view (see for instance [16,22]). However this fruitful linearisation has, so far, been limited to the above "vertical" square functions estimates, leaving aside the "conical" estimates of the form (1.2)…”

Section: Introductionmentioning

confidence: 99%

Conical square function estimates in UMD Banach spaces and applications to H ∞-functional calculi

2008

View full text Add to dashboard Cite

Abstract. We study conical square function estimates for Banach-valued functions, and introduce a vector-valued analogue of the Coifman-Meyer-Stein tent spaces. Following recent work of Auscher-M c Intosh-Russ, the tent spaces in turn are used to construct a scale of vector-valued Hardy spaces associated with a given bisectorial operator A with certain off-diagonal bounds, such that A always has a bounded H ∞ -functional calculus on these spaces. This provides a new way of proving functional calculus of A on the Bochner spaces L p (R n ; X) by checking appropriate conical square function estimates, and also a conical analogue of Bourgain's extension of the Littlewood-Paley theory to the UMDvalued context. Even when X = C, our approach gives refined p-dependent versions of known results.

show abstract

On square functions associated to sectorial operators

Abstract: Abstract. -We give new results on square functions

Cited by 44 publications

References 17 publications

Square functions, bounded analytic semigroups, and applications

Square functions, bounded analytic semigroups, and applications

Maximal inequalities and Riesz transform estimates on L^p spaces for Schrödinger operators with nonnegative potentials

Conical square function estimates in UMD Banach spaces and applications to H ∞-functional calculi

Contact Info

Product

Resources

About