Beurling–Ahlfors extension by heat kernel, A∞‐weights for VMO, and vanishing Carleson measures

Wei, Huaying; Matsuzaki, Katsuhiko

doi:10.1112/blms.12454

Cited by 12 publications

(11 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Thus, the bi-Lipschitz constant L of F depends only on ρ and K by ( 15) and ( 16). Moreover, again in the proof of [30,Theorem 3.3], we see that K also depends only on ρ. If u * < C JN , then e u ∈ A 2 and the A 2 -constant is given in terms of u * as is shown in Proposition 2.1.…”

Section: The Variant Of the Beurling-ahlfors Extension For Bmosupporting

confidence: 55%

The $p$-Weil-Petersson Teichmüller space and the quasiconformal extension of curves

Wei,

Matsuzaki

2021

Preprint

Self Cite

View full text Add to dashboard Cite

We consider the correspondence between the space of p-Weil-Petersson curves γ on the plane and the p-Besov space of u = log γ ′ on the real line for p ≥ 2. We prove that the variant of the Beurling-Ahlfors extension defined by using the heat kernel yields a holomorphic map for u on a domain of the p-Besov space to the space of p-integrable Beltrami coefficients. This in particular gives a global real-analytic section for the Teichmüller projection from the space of p-integrable Beltrami coefficients to the p-Weil-Petersson Teichmüller space.

show abstract

Section: The Variant Of the Beurling-ahlfors Extension For Bmosupporting

confidence: 55%

The $p$-Weil-Petersson Teichmüller space and the quasiconformal extension of curves

Wei,

Matsuzaki

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…The former statement of the next theorem follows from [14,Theorem 4.2]. See [37,Theorem 3.4] for its exposition. The latter statement is given in [39].…”

Section: 3mentioning

confidence: 90%

BMO embeddings, chord-arc curves, and Riemann mapping parametrization

Wei¹,

Matsuzaki²

2021

Preprint

Self Cite

View full text Add to dashboard Cite

We consider the space of chord-arc curves on the plane passing through the infinity with their parametrization γ on the real line, and embed this space into the product of the BMO Teichmüller spaces. The fundamental theorem we prove about this representation is that log γ ′ also gives a biholomorphic homeomorphism into the complex Banach space of BMO functions. Using these two equivalent complex structures, we develop a clear exposition on the analytic dependence of involved mappings between certain subspaces. Especially, we examine the parametrization of a chord-arc curve by using the Riemann mapping and its dependence on the arc-length parametrization. As a consequence, we can solve a conjecture of Katznelson, Nag, and Sullivan in 1990 by showing that this dependence is not continuous.

show abstract

“…In this case, the extension F : U → U of γ : R → R is the variant of Beurling-Ahlfors extension by heat kernel. The following results are obtained in [13, Theorem 4.2] and [29,30].…”

Section: The Variant Of Beurling-ahlfors Extension By Heat Kernelmentioning

confidence: 95%

The VMO-Teichmüller space and the variant of Beurling-Ahlfors extension by heat kernel

Wei¹,

Matsuzaki²

2021

Preprint

Self Cite

View full text Add to dashboard Cite

We give a real-analytic section for the Teichmüller projection onto the VMO-Teichmüller space by using the variant of Beurling-Ahlfors extension by heat kernel introduced by Fefferman, Kenig and Pipher in 1991. Based on this result, we prove that the VMO-Teichmüller space can be endowed with a real Banach manifold structure that is real-analytically equivalent to its complex Banach manifold structure. We also obtain that the VMO-Teichmüller space admits a real-analytic contraction mapping.

show abstract

Beurling–Ahlfors extension by heat kernel, A∞‐weights for VMO, and vanishing Carleson measures

Cited by 12 publications

References 8 publications

The $p$-Weil-Petersson Teichmüller space and the quasiconformal extension of curves

The $p$-Weil-Petersson Teichmüller space and the quasiconformal extension of curves

BMO embeddings, chord-arc curves, and Riemann mapping parametrization

The VMO-Teichmüller space and the variant of Beurling-Ahlfors extension by heat kernel

Contact Info

Product

Resources

About