In this paper, we study two types of weighted Hardy–Littlewood–Sobolev (HLS) inequalities, also known as Stein–Weiss inequalities, on the Heisenberg group. More precisely, we prove the |u| weighted HLS inequality in Theorem 1.1 and the |z| weighted HLS inequality in Theorem 1.5 (where we have denoted u = (z, t) as points on the Heisenberg group). Then we provide regularity estimates of positive...

In this study, by a non-negative homogeneous kernel k we prove some extensions of Hardy's inequalityin two and three dimensions

in this study, by a non-negative homogeneous kernel k we prove some extensions of hardy's inequalityin two and three dimensions

We consider the second best constant in Hardy-Sobolev inequality on a Riemannian manifold. More precisely, we are interested with existence of extremal functions for this inequality. This problem was tackled by Djadli-Druet [5] Sobolev inequalities. Here, establish corresponding result singular case. In addition, perform blow-up analysis solutions equations minimizing type. yields informations ...

Abstract By the use of weight coefficients, idea introduced parameters and technique real analysis, a more accurate Hilbert-type inequality in whole plane with general homogeneous kernel is given, which an extension Hardy–Hilbert’s inequality. An equivalent form obtained. The statements best possible constant factor related to several parameters, operator expressions few particular cases are co...

The diamagnetic inequality is established for the Schrödinger operator H 0 in L (R), d = 2, 3, describing a particle moving in a magnetic field generated by finitely or infinitely many Aharonov-Bohm solenoids located at the points of a discrete set in R, e.g., a lattice. This fact is used to prove the Lieb-Thirring inequality as well as CLR-type eigenvalue estimates for the perturbed Schrödinge...

The diamagnetic inequality is established for the Schrödinger operator H 0 in L (R), d = 2, 3, describing a particle moving in a magnetic field generated by finitely or infinitely many Aharonov-Bohm solenoids located at the points of a discrete set in R, e.g., a lattice. This fact is used to prove the Lieb-Thirring inequality as well as CLR-type eigenvalue estimates for the perturbed Schrödinge...

We obtain Fourier inequalities in the weighted Lp spaces for any 1<p<∞ involving Hardy–Cesàro and Hardy–Bellman operators. extend these results to product Hardy p⩽1. Moreover, boundedness of Hardy-Cesàro Hardy-Bellman operators various (Lebesgue, Hardy, BMO) is discussed. One our main tools an appropriate version Hardy–Littlewood–Paley inequality ‖fˆ‖Lp′,q≲‖f‖Lp,q.

Let {cj} be a null sequence of bounded variation. We give appreciate smoothness and growth conditions on {cj} to obtain the pointwise convergence as well as Lr -convergence of Laguerre series ∑ cj a j . Then, we prove aHardy-Littlewood type inequality ∫∞ 0 |f(t)|r dt≤ C ∑∞ j=0 |cj| j̄1−r/2 for certain r ≤ 1, where f is the limit function of ∑ cj a j . Moreover, we show that if f(x) ∼ ∑cj a j is ...

The classical embedding theorem of Carleson deals with finite positive Borel measures μ on the closed unit disk for which there exists a positive constant c such that ‖f‖L2(μ) ≤ c‖f‖H2 for all f ∈ H, the Hardy space of the unit disk. Lefèvre et al. examined measures μ for which there exists a positive constant c such that ‖f‖L2(μ) ≥ c‖f‖H2 for all f ∈ H. The first type of inequality above was e...