Results 11 to 20 of about 12,592 (145)
Reversed Hardy-Littlewood-Sobolev inequalities with weights on the Heisenberg group
Advances in Nonlinear Analysis, 2023 In this article, we establish some reverse weighted Hardy-Littlewood-Sobolev inequalities on the Heisenberg group. We then show the existence of extremal functions for the above inequalities by combining the subcritical approach and the renormalization ...
Hu Yunyun
doaj +2 more sources
Generalising the Hardy-Littlewood Method for Primes
, 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 Corput giving an asymptotic for the number of 3-term progressions of primes, all less than N.
Green, Ben
openaire +6 more sources
Rearrangement Free Method for Hardy-Littlewood-Sobolev Inequalities on $\mathbb{S}^n$
Analysis in Theory and Applications, 2022 Summary: For conformal Hardy-Littlewood-Sobolev (HLS) inequalities [\textit{E. H. Lieb}, Ann. Math. (2) 118, 349--374 (1983; Zbl 0527.42011)] and reversed conformal HLS inequalities [\textit{J. Dou} and \textit{M. Zhu}, Int. Math. Res. Not. 2015, No. 19, 9696--9726 (2015; Zbl 1329.26033)] on \(\mathbb{S}^n\), a new proof is given for the attainability ...
Zhang, Shutao, Han, Yazhou
openaire +1 more source
Integral inequalities with an extended Poisson kernel and the existence of the extremals
Advanced Nonlinear Studies, 2023 In this article, we first apply the method of combining the interpolation theorem and weak-type estimate developed in Chen et al. to derive the Hardy-Littlewood-Sobolev inequality with an extended Poisson kernel.
Tao Chunxia, Wang Yike
doaj +1 more source
Local Muckenhoupt class for variable exponents
Journal of Inequalities and Applications, 2021 This work extends the theory of Rychkov, who developed the theory of A p loc $A_{p}^{\mathrm{loc}}$ weights. It also extends the work by Cruz-Uribe SFO, Fiorenza, and Neugebauer. The class A p ( ⋅ ) loc $A_{p(\cdot )}^{\mathrm{loc}}$ is defined.
Toru Nogayama, Yoshihiro Sawano
doaj +1 more source
On the Waring-Goldbach problem for two squares and four cubes
Open Mathematics, 2023 Let NN be a sufficiently large integer. In this article, it is proved that, with at most O(N112+ε)O\left({N}^{\tfrac{1}{12}+\varepsilon }) exceptions, all even positive integers up to NN can be represented in the form p12+p22+p33+p43+p53+p63{p}_{1}^{2 ...
Zhang Min, Bai Hongxin, Li Jinjiang
doaj +1 more source
Diophantine approximation with one prime, two squares of primes and one kth power of a prime
Open Mathematics, 2021 Let ...
Gambini Alessandro
doaj +1 more source
On Waring's problem: some consequences of Golubeva's method [PDF]
, 2012 We investigate sums of mixed powers involving two squares, two cubes, and various higher powers, concentrating on situations inaccessible to the Hardy-Littlewood ...
Wooley, Trevor D.
core +2 more sources
Hamiltonian cycles in torical lattices [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 We establish sufficient conditions for a toric lattice $T_{m,n}$ to be Hamiltonian. Also, we give some asymptotics for the number of Hamiltonian cycles in $T_{m,n}$.
Vladimir K. Leontiev
doaj +1 more source
Bihomogeneous forms in many variables [PDF]
, 2013 We count integer points on bihomogeneous varieties using the Hardy-Littlewood method. The main novelty lies in using the structure of bihomogeneous equations to obtain asymptotics in generically fewer variables than would be necessary in using the ...
Schindler, Damaris
core +2 more sources