Beltrami operators in the plane

By Kari ASTALA *, Tadeusz Iwaniec, Eero Saksman. 2001

163 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/a284e832cd6f0027138652e59d9d5349d17906ad

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In Applied Mathematics

In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

SHARP WEIGHTED BOUNDS FOR FRACTIONAL INTEGRAL OPERATORS (2009, background): “e known. The interest in sharp weighted norm for singular integral operators is motivated in part by applications in partial diﬀerential equations. We refer the reader to Astala, Iwaniec, and Saksman [1]; and Petermichl and Volberg [23] for such applications. Petermichl [21], [22] showed that (1.3) ”
Calderon's inverse conductivity problem in the plane (2006, background): “2 also has nonlinear counterparts [4] yielding solutions to nonlinear uniformly elliptic PDE’s; here see also [15], [5].”
Fractional Differentiability for Solutions of Nonlinear Elliptic Equations (2016, background): “The number p0 was precisely described in [1] when n = s = 2, and is unknown otherwise.”
Extra cancellation of even Calderón–Zygmund operators and quasiconformal mappings (2008, background): “42–43] in the context of L spaces, which has been further exploited in [5].”
Quantitative weighted estimates for rough homogeneous singular integrals (2015, background): “Saksman [1] raised the question whether the norm ‖B‖Lp(w)→Lp(w) depends linearly on [w]Ap , p ≥ 2.”
SHARP BOUNDS FOR GENERAL COMMUTATORS ON WEIGHTED LEBESGUE SPACES (2010, unknown): “This problem has attracted renewed attention because of the work of Astala, Iwaniec and Saksman [2].”
Sparse bilinear forms for Bochner Riesz multipliers and applications (2016, unknown): “See for example Feﬀerman-Kenig-Pipher [18], Astala-Iwaniec-Saksman [1], Petermichl-Volberg [31].”
The sharp bound for the Hilbert transform on weighted Lebesgue spaces in terms of the classical A p characteristic (2007, background): “In [1], the question was asked, what happend for the borderline case q = 1 + k? We showed that the solution is still always continuous and, thus, is a quasiregular map.”
The sharp weighted bound for general Calderón-Zygmund operators (2010, background): “for some further numbers πIJ ∈ [0, 1] related to conditional probabilities as before.”
Sharp weighted norm estimates beyond Calderón–Zygmund theory (2015, unknown): “See for example Fefferman, Kenig and Pipher [Fefferman et al. 1991] and Astala, Iwaniec and Saksman [Astala et al. 2001].”
Sharp weighted estimates for approximating dyadic operators (2010, background): “More recently, this problem has attracted renewed attention because of the work of Astala, Iwaniec and Saksman [1].”
Representation of singular integrals by dyadic operators, and the A_2 theorem (2011, background): “One of the key original motivations to study the A2 theorem was a conjecture of Astala–Iwaniec–Saksman [1] concerning the special case where T is the Ahlfors–Beurling operator Bf(z) := − 1 π p. v. ˆ C 1 ζ2 f(z − ζ) dA(ζ), and A is the area measure (two-dimensional Lebesgue measure) on C ≃ R2.”