Maximal Functions Associated to Filtrations

By Michael Christ, Alexander V. Kiselev. 2001

477 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8ef33a7cb3e074ea017fd074132ccdebc6de77fb

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In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Weighted Strichartz estimates with angular regularity and their applications (2008, background): “2 in [7]), we can get the inhomogeneous estimates.”
A Carleson type theorem for a Cantor group model of the scattering transform (2002, background): “Beals and Coifman [2] study in detail the case when the potential is (generic) in L1 or in weighted spaces L1 ∩ L2 with weights of the form (1 + |x|)m for suitable m.”
Concerning the wave equation on asymptotically Euclidean manifolds (2008, methodology): “Since q > 2, we can apply the Christ-Kiselev lemma [5] to conclude the proof.”
Sharp Strichartz estimates on nontrapping asymptotically conic manifolds (2004, methodology): “In this section we prove a minor variant of the Christ-Kiselev lemma [7].”
The cubic nonlinear Schr\"odinger equation in two dimensions with radial data (2007, background): “In a series of papers culminating in [12], Christ and Kiselev proved that under certain hypotheses, truncations of bounded integral operators are themselves bounded.”
On the Cauchy Problem for the Generalized Korteweg-de Vries Equation (2003, background): “A proof of the above statement can be found in Christ and Kiselev (1998), Smith andSogge (2000) in the context ofL q t L r x spaces.”
On the local well-posedness of the Benjamin-Ono and modified Benjamin-Ono equations (2003, background): “A useful lemma of Christ and Kiselev ([ ChKi ]) allows one to deduce the inequalities (2.8) and (2.10) from the corresponding “nonretarded” ones.”
STRICHARTZ ESTIMATES FOR A SCHRÖDINGER OPERATOR WITH NONSMOOTH COEFFICIENTS (2002, methodology): “With the exception of the end-point result (which corresponds to q ¼ 2) one can give a very simple proof of the theorem using a lemma of Christ and Kiselev.”
THE GENERALIZED KORTEWEG–DE VRIES EQUATION ON THE HALF LINE (2001, methodology): “1 in [7]: Define Yn = [0, tn], so that Yn ⊆ Yn+1.”
Global well-posedness and scattering for the defocusing, L2-critical, nonlinear Schrödinger equation when d = 1 (2010, background): “See [80] for p = q = 6, [19, 40, 50, 85, 102] This result also holds in the more general case in which the supports of ˆ v 0 ( ξ ) and ˆ u 0 ( ξ ) are separated by a distance | ξ | ∼ N .”
Strichartz estimates for the wave equation on manifolds with boundary (2008, background): “A lemma of Christ-Kiselev [ 7 ] allows one to deduce inhomogeneous Strichartz estimates from the homogeneous estimates.”