Levy processes and Fourier multipliers

By Rodrigo Bañuelos, Krzysztof Bogdan. 2006

86 citations recorded by the source corpus.

Abstract We study Fourier multipliers which result from modulating jumps of Levy processes. Using the theory of martingale transforms we prove that these operators are bounded in L p ( R d ) for 1 p ∞ and we obtain the same explicit bound for their norm as the one known for the second order Riesz transforms.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/520d2a4575e2dfe26cb284e80ebb7d2aa43860ac

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

A relatively short proof of Itô’s formula for SPDEs and its applications (2012, methodology): “p pp (Rd) . The lemma is proved. For a bounded measurable m(y),y ∈Rd,and α∈(0,2), set for v ∈ S(Rd),x∈Rd, Lv(x) = Lαv(x) = Z ∇αv(x)m(y) dy |y|d+α . We will need the following continuity estimate (see [2] for a symmetric case, Theorem 2.1 in [5] for a general case using H¨older estimates, and Lemma 1”
The foundational inequalities of D.L. Burkholder and some of their ramifications (2010, background): “Then Vf (Zt) = Vf (Xt, T − t), 0 < t < T is a martingale (see [14], Lemmas 1-4) and it follows from the general Itô formula ([60, 139]) that Vf (Zt)− Vf (Z0) = ∑”