Hardy Spaces of Holomorphic Functions for Domains in ℂ n with Minimal Smoothness

Lanzani, Loredana; Stein, Elias M.

doi:10.1007/978-3-319-30961-3_11

Cited by 7 publications

(4 citation statements)

References 52 publications

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“…More recently, L. Lanzani and E. M. Stein studied the regularity of the Szegö projection on strongly pseudoconvex domains with minimal boundary regularity, [15,16], obtaining the L p -boundedness for 1 < p < ∞.…”

Section: Introduction and Statement Of The Main Resultsmentioning

confidence: 99%

Regularity of the Szegö projection on model worm domains

Monguzzi

Peloso

2017

Complex Variables and Elliptic Equations

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In this paper we study the regularity of the Szegö projection on Lebesgue and Sobolev spaces on the boundary of the unbounded model worm domain D ′ β . We consider the Hardy spaceLet W s,p (bD ′ β ) denote the Lebesgue-Sobolev space on bD ′ β . We prove that P , initially defined on the dense subspace W s,p (bD ′ β ) ∩ L 2 (bD ′ β , dσ), extends to a bounded operator P : W s,p (bD ′ β ) → W s,p (bD ′ β ), for 1 < p < ∞ and s ≥ 0.

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Section: Introduction and Statement Of The Main Resultsmentioning

confidence: 99%

Regularity of the Szegö projection on model worm domains

Monguzzi

Peloso

2017

Complex Variables and Elliptic Equations

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“…As is well known, the holomorphic Hardy space H p (bD), defined as in e.g. [25,34,46], is a closed proper subspace of L p (bD) for any 1 ≤ p ≤ ∞. In the special case p = 2, Hilbert space theory grants the existence of a unique orthogonal projection S σ : L 2 (bD) → H 2 (bD) known in the literature as the Cauchy-Szegő projection, which is bounded with minimal norm S σ = 1.…”

Section: Introduction and Statement Of Main Resultsmentioning

confidence: 99%

Commutators of Cauchy-Szego type integrals for domains in C^n with minimal smoothness

Duong¹,

Lacey

Li³

et al. 2021

Indiana Univ. Math. J.

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Let D ⊂ C n be a bounded, strongly pseudoconvex domain whose boundary bD satisfies the minimal regularity condition of class C 2 . We characterize boundedness and compactness in L p (bD, ω), for 1 < p < ∞, of the commutator [b, Sω] where Sω is the Cauchy-Szegő (orthogonal) projection of L 2 (bD, ω) onto the holomorphic Hardy space H 2 (bD, ω) and the measure ω belongs to a family (the "Leray Levi-like" measures) that includes induced Lebesgue measure σ. We next consider a much larger family of measures {Ω} modeled after the Muckenhoupt weights for σ: we define the holomorphic Hardy spaces H p (bD, Ω) for any Ap-like measure Ω and we characterize boundedness and compactness of [b, SΩ] in L 2 (bD, Ω) for any A2-like measure Ω. Earlier closely related results rely upon an asymptotic expansion, and subsequent pointwise estimates, of the Cauchy-Szegő kernel that are not available in the settings of minimal regularity of bD and/or Ap-like measures.Among the new main tools are • operator identities for [b, Sω] and for [b, SΩ] inspired by the classical Kerzman-Stein equation for Sσ in L 2 (bD, σ) [22] and its 2017 variant in L p (bD, ω) [32], where p = 2; • sharp weighted estimates in L p (bD, Ω) for a family of Cauchy type integral operators {Cǫ}ǫ (related to SΩ via the Kerzman-Stein equations) and for their commutators {[b, Cǫ]}ǫ; • cancellation estimates in L p (bD, Ω) for the symmetrized truncation of the aforementioned {Cǫ}ǫ with quantitative norm bounds displaying explicit dependence on ǫ.

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“…Recently L. Lanzani and E.M. Stein in [14] proved that strict pseudoconvexity of domain Ω implies that functions holomorphic in neighbourhood of Ω are dense in H p (Ω) with 1 < p < ∞ even if the defining function is C 2 −smooth. Also every holomorphic in neighbourhood of Ω function can be approximated on Ω by polynomials since Ω is Runge.…”

Section: Pseudoanalytic Continuation By Global Polynomial Approximationsmentioning

confidence: 99%

“…We denote the space of holomorphic functions as H(Ω) and consider the Hardy space (see [5,14,23,24])…”

Section: Introductionmentioning

confidence: 99%

Constructive description of analytic Besov spaces in strictly pseudoconvex domains

Rotkevich

2021

Anal.Math.Phys.

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Hardy Spaces of Holomorphic Functions for Domains in ℂ n with Minimal Smoothness

Cited by 7 publications

References 52 publications

Regularity of the Szegö projection on model worm domains

Regularity of the Szegö projection on model worm domains

Commutators of Cauchy-Szego type integrals for domains in C^n with minimal smoothness

Constructive description of analytic Besov spaces in strictly pseudoconvex domains

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