Calderón-Zygmund Capacities and Operators on Nonhomogeneous Spaces

By Alexander Volberg. 2003

188 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/064b9a40aaceabe20d4fe399bbbc0d07a0392d60

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In Applied Mathematics

Citations in the corpus

Two weight estimate for the Hilbert transform and corona decomposition for non-doubling measures (2010, background): “Now to say ∫ Q |TχQ| 2dx ≤ C|Q| we need the estimate ∫ Q |Tχ2Q\Q| 2dx ≤ C|Q|, which is immediate again from the same roughest estimate of Calderón–Zygmund kernel.”
Two weight norm inequalities for fractional integral operators and commutators (2014, methodology): “[101] A. Volberg.”
Sharp weighted estimates of the dyadic shifts and $A_2$ conjecture (2010, methodology): “The idea of such decomposition goes back to methods of non-homogeneous Harmonic Analysis exploited in [26] or [41] for example.”
Discrete Hilbert transforms on sparse sequences (2009, background): “the discussion in the last three chapters of [31]).”
Two Weight Inequality for the Hilbert Transform: A Real Variable Characterization, II (2012, methodology): “To make the two reductions below, one must make a random selection of grids, as is detailed in [8, 29].”
Bergman-type singular integral operators and the characterization of Carleson measures for Besov-Sobolev spaces on the complex ball (2009, methodology): “Treil, and the first author in the series of papers [13, 14, 15, 16] and further explained in the book by the first author [25].”
Sharp weighted estimates for classical operators (2010, background): “When p = 2, Theorem 1.8 was proved by Wittwer [57] and by Hukovic, Treil and Volberg [22]; this was extended to p < 2 by extrapolation in [12] and examples were given to show that in this range the exponent is the best possible.”
A characterization of two weight norm inequalities for maximal singular integrals with one doubling measure (2008, methodology): “Consequently, characterizations are given in [24] and [10] for the Hilbert transform and Riesz transforms in weighted L(2) spaces under various additional hypotheses.”
Rectifiability of harmonic measure (2015, unknown): “This result follows from the deep non-homogeneous Tb theorem of Nazarov, Treil and Volberg in [NTrV] (see also [Vo]) in combination with the methods in [To1].”
New maximal functions and multiple weights for the multilinear Calderón-Zygmund theory (2009, methodology): “We refer to Coifman–Meyer [12], Christ [6], Fefferman [20], Stein [48], Grafakos–Torres [27] and Volberg [49] for surveys and historical details about these different aspects of the subject.”