Harmonic Analysis
http://hdl.handle.net/20.500.11824/3
Wed, 21 Oct 2020 02:57:01 GMT2020-10-21T02:57:01ZSparse and weighted estimates for generalized Hörmander operators and commutators
http://hdl.handle.net/20.500.11824/1185
Sparse and weighted estimates for generalized Hörmander operators and commutators
Ibañez-Firnkorn G.H.; Rivera-Ríos I.P.
In this paper a pointwise sparse domination for generalized Ho ̈rmander and also for iterated commutators with those operators is provided generalizing the sparse domination result in [24]. Relying upon that sparse domination a number of quantitative estimates are derived. Some of them are improvements and complementary results to those contained in a series of papers due to M. Lorente, J. M. Martell, C. P ́erez, S. Riveros and A. de la Torre [29, 28, 27]. Also the quantitative endpoint estimates in [24] are extended to iterated commutators. Other results that are obtained in this work are some local exponential decay estimates for generalized Ho ̈rmander operators in the spirit of [33] and some negative results concerning Coifman-Fefferman estimates for a certain class of kernels satisfying particular generalized Ho ̈rmander conditions.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/20.500.11824/11852019-01-01T00:00:00ZMultilinear singular integrals on non-commutative lp spaces
http://hdl.handle.net/20.500.11824/1173
Multilinear singular integrals on non-commutative lp spaces
Di Plinio F.; Li K.; Martikainen H.; Vuorinen E.
We prove Lp bounds for the extensions of standard multilinear Calderón- Zygmund operators to tuples of UMD spaces tied by a natural product structure. The product can, for instance, mean the pointwise product in UMD function lattices, or the composition of operators in the Schatten-von Neumann subclass of the algebra of bounded operators on a Hilbert space. We do not require additional assumptions beyond UMD on each space – in contrast to previous results, we e.g. show that the Rademacher maximal function property is not necessary. The obtained generality allows for novel applications. For instance, we prove new versions of fractional Leibniz rules via our results concerning the boundedness of multilinear singular integrals in non-commutative Lp spaces. Our proof techniques combine a novel scheme of induction on the multilinearity index with dyadic-probabilistic techniques in the UMD space setting.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/20.500.11824/11732019-01-01T00:00:00ZThe observational limit of wave packets with noisy measurements
http://hdl.handle.net/20.500.11824/1144
The observational limit of wave packets with noisy measurements
Caro P.; Meroño C.
The authors consider the problem of recovering an observable from certain measurements containing random errors. The observable is given by a pseudodifferential operator while the random errors are generated by a Gaussian white noise. The authors show how wave packets can be used to partially recover the observable from the measurements almost surely. Furthermore, they point out the limitation of wave packets to recover the remaining part of the observable, and show how the errors hide the signal coming from the observable. The recovery results are based on an ergodicity property of the errors produced by wave packets.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/20.500.11824/11442019-01-01T00:00:00ZScattering with critically-singular and δ-shell potentials
http://hdl.handle.net/20.500.11824/1143
Scattering with critically-singular and δ-shell potentials
Caro P.; García A.
The authors consider a scattering problem for electric potentials that have a component which is critically singular in the sense of Lebesgue spaces, and a component given by a measure supported on a compact Lipschitz hypersurface. They study direct and inverse point-source scattering under the assumptions that the potentials are real-valued and compactly supported. To solve the direct scattering problem, the authors introduce two functional spaces ---sort of Bourgain type spaces--- that allow to refine the classical resolvent estimates of Agmon and Hörmander, and Kenig, Ruiz and Sogge. These spaces seem to be very useful to deal with the critically-singular and δ-shell components of the potentials at the same time. Furthermore, these spaces and their corresponding resolvent estimates turn out to have a strong connection with the estimates for the conjugated Laplacian used in the context of the inverse Calderón problem. In fact, the authors derive the classical estimates by Sylvester and Uhlmann, and the more recent ones by Haberman and Tataru after some embedding properties of these new spaces. Regarding the inverse scattering problem,the authors prove uniqueness for the potentials from point-source scattering data at fix energy. To address the question of uniqueness the authors combine some of the most advanced techniques in the construction of complex geometrical optics solutions.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/20.500.11824/11432019-01-01T00:00:00Z