Analysis of Partial Differential Equations (APDE)
http://hdl.handle.net/20.500.11824/1
Sat, 09 Dec 2023 19:00:30 GMT2023-12-09T19:00:30ZWeighted BMO estimates for singular integrals and endpoint extrapolation in Banach function spaces
http://hdl.handle.net/20.500.11824/1691
Weighted BMO estimates for singular integrals and endpoint extrapolation in Banach function spaces
Nieraeth, Z.; Rey, G.
In this paper we prove sharp weighted BMO estimates for singular integrals, and we show how such estimates can be extrapolated to Banach function spaces.
Mon, 01 May 2023 00:00:00 GMThttp://hdl.handle.net/20.500.11824/16912023-05-01T00:00:00ZWeighted Lorentz spaces: Sharp mixed A<inf>p</inf> − A<inf>∞</inf> estimate for maximal functions
http://hdl.handle.net/20.500.11824/1689
Weighted Lorentz spaces: Sharp mixed A<inf>p</inf> − A<inf>∞</inf> estimate for maximal functions
Accomazzo, N.; Duoandikoetxea, J.; Nieraeth, Z.; Ombrosi, S.; Pérez, C.
We prove the sharp mixed Ap−A∞ weighted estimate for the Hardy-Littlewood maximal function in the context of weighted Lorentz spaces, namely [Formula presented] where [Formula presented]. Our method is rearrangement free and can also be used to bound similar operators, even in the two-weight setting. We use this to also obtain new quantitative bounds for the strong maximal operator and for M in a dual setting.
Wed, 15 Mar 2023 00:00:00 GMThttp://hdl.handle.net/20.500.11824/16892023-03-15T00:00:00ZExtrapolation in general quasi-Banach function spaces
http://hdl.handle.net/20.500.11824/1688
Extrapolation in general quasi-Banach function spaces
Nieraeth, Z.
In this work we prove off-diagonal, limited range, multilinear, vector-valued, and two-weight versions of the Rubio de Francia extrapolation theorem in general quasi-Banach function spaces. We prove mapping properties of the generalization of the Hardy-Littlewood maximal operator to very general bases that includes a method to obtain self-improvement results that are sharp with respect to its operator norm. Furthermore, we prove bounds for the Hardy-Littlewood maximal operator in weighted Lorentz, variable Lebesgue, and Morrey spaces, and recover and extend several extrapolation theorems in the literature. Finally, we provide an application of our results to the Riesz potential and the Bilinear Hilbert transform.
Wed, 15 Nov 2023 00:00:00 GMThttp://hdl.handle.net/20.500.11824/16882023-11-15T00:00:00ZALMOST SURE POINTWISE CONVERGENCE OF THE CUBIC NONLINEAR SCHRODINGER EQUATION ON ̈ T 2
http://hdl.handle.net/20.500.11824/1685
ALMOST SURE POINTWISE CONVERGENCE OF THE CUBIC NONLINEAR SCHRODINGER EQUATION ON ̈ T 2
Lucà, R.
We revisit a result from “Pointwise convergence of the Schr ̈odinger
flow, E. Compaan, R. Luc`a, G. Staffilani, International Mathematics Research
Notices, 2021 (1), 596-647” regarding the pointwise convergence of solutions
to the periodic cubic nonlinear Schr ̈odinger equation in dimension d = 2.
Sat, 01 Jan 2022 00:00:00 GMThttp://hdl.handle.net/20.500.11824/16852022-01-01T00:00:00Z