Generalising the Hardy-Littlewood Method for Primes [PDF]
, 2006 The Hardy-Littlewood method is a well-known technique in analytic number theory. Among its spectacular applications are Vinogradov's 1937 result that every sufficiently large odd number is a sum of three primes, and a related result of Chowla and Van der
Green, Ben
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A Hardy–Littlewood–Sobolev-Type Inequality for Variable Exponents and Applications to Quasilinear Choquard Equations Involving Variable Exponent [PDF]
Mediterranean Journal of Mathematics, 2019 In this work, we have proved a Hardy–Littlewood–Sobolev inequality for variable exponents. After that, we use this inequality together with the variational method to establish the existence of solution for a class of Choquard equations involving the p(x)-
C. O. Alves, L. S. Tavares
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Fractional Sobolev and Hardy-Littlewood-Sobolev inequalities [PDF]
, 2014 This work focuses on an improved fractional Sobolev inequality with a remainder term involving the Hardy-Littlewood-Sobolev inequality which has been proved recently. By extending a recent result on the standard Laplacian to the fractional case, we offer
Jankowiak, Gaspard, Nguyen, Van Hoang
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Optimal control of singular Fourier multipliers by maximal operators [PDF]
, 2013 We control a broad class of singular (or "rough") Fourier multipliers by geometrically-defined maximal operators via general weighted $L^2(\mathbb{R})$ norm inequalities. The multipliers involved are related to those of Coifman--Rubio de Francia--Semmes,
Bennett, Jonathan
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Sharp criteria of Liouville type for some nonlinear systems [PDF]
, 2013 In this paper, we establish the sharp criteria for the nonexistence of positive solutions to the Hardy-Littlewood-Sobolev (HLS) type system of nonlinear equations and the corresponding nonlinear differential systems of Lane-Emden type equations.
Y. Lei, Congming Li
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Mixed weak type estimates: Examples and counterexamples related to a problem of E. Sawyer [PDF]
, 2016 We study mixed weighted weak-type inequalities for families of functions, which can be applied to study classical operators in harmonic analysis. Our main theorem extends the key result from D. Cruz-Uribe, J.M. Martell and C.
Ombrosi, Sheldy, Perez, Carlos
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Shooting with degree theory: Analysis of some weighted poly-harmonic systems [PDF]
, 2014 In this paper, the author establishes the existence of positive entire solutions to a general class of semilinear poly-harmonic systems, which includes equations and systems of the weighted Hardy--Littlewood--Sobolev type.
Villavert, John
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Subdyadic square functions and applications to weighted harmonic analysis [PDF]
, 2016 Through the study of novel variants of the classical Littlewood-Paley-Stein $g$-functions, we obtain pointwise estimates for broad classes of highly-singular Fourier multipliers on $\mathbb{R}^d$ satisfying regularity hypotheses adapted to fine ...
Beltran, David, Bennett, Jonathan
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Estimates for Smooth Weyl Sums on Major Arcs [PDF]
International mathematics research noticesWe present estimates for smooth Weyl sums of use on sets of major arcs in applications of the Hardy–Littlewood method. In particular, we derive mean value estimates on major arcs for smooth Weyl sums of degree $k$ delivering essentially optimal bounds ...
Joerg Bruedern, T. Wooley
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Restriction theory of the Selberg sieve, with applications [PDF]
, 2004 The Selberg sieve provides majorants for certain arithmetic sequences, such as the primes and the twin primes. We prove an L^2-L^p restriction theorem for majorants of this type.
Green, Ben, Tao, Terence
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