Related papers: A note on a two-weight estimate for the dyadic squ…

In a recent work by A. Martini and A. Sikora (arXiv:1204.1159), sharp L^p spectral multiplier theorems for the Grushin operators acting on $R^{d_1} \times R^{d_2}$ are obtained in the case $d_1 \geq d_2$. Here we complete the picture by…

In this paper, we give an explicit formula of the Shintani double zeta functions with any ramification in the most general setting of adeles over an arbitrary number field. Three applications of the explicit formula are given. First, we…

This paper presents a new proof of the results regarding the continuity of weighted estimates with respect to the characteristic of the weight. Here we first prove the result in the dyadic case which is "easier" and then by the use of the…

We prove a Log Log inequality with a sharp constant in four dimensions for radially symmetric functions. We also show that the constant in the Log estimate is almost sharp.

In this paper we obtain the average sensitivity of the laced Boolean functions. This confirms a conjecture of Shparlinski. We also compute the weights of the laced Boolean functions and show that they are almost balanced.

Weighted quadratic estimates are proved for certain bisectorial firstorder differential operators with bounded measurable coefficients which are (not necessarily pointwise) accretive, on complete manifolds with positive injectivity radius.…

The current status concerning Hardy-type inequalities with sharp constants is presented and described in a unified convexity way. In particular, it is then natural to replace the Lebesgue measure $dx$ with the Haar measure $dx/x.$ There are…

In this short note, we prove a sharp quantization for positive solutions of Lane-Emden problems in a bounded planar domain. This result has been conjectured by De Marchis, Ianni and Pacella [6, Remark 1.2].

We establish power saving asymptotics for the sum of the divisor function along a binary quartic form, improving on work of Daniel. The proof involves an application of a recent two dimensional delta method due to Li, Rydin-Myerson, and…

Let $S_{\alpha}$ be the multilinear square function defined on the cone with aperture $\alpha \geq 1$. In this paper, we investigate several kinds of weighted norm inequalities for $S_{\alpha}$. We first obtain a sharp weighted estimate in…

The well known duality between the Sobolev inequality and the Hardy-Littlewood-Sobolev inequality suggests that the Nash inequality could also have an interesting dual form, even though the Nash inequality relates three norms instead of…

In this note, we obtain the rigidity of the sharp Cheng-Yau gradient estimate for positive harmonic functions on surfaces with nonegative Gaussian curvature, the rigidity of the sharp Li-Yau gradient estimate for positive solutions to heat…

For certain non compact Riemannian manifolds with ends, we obtain Littlewood-Paley type estimates on (weighted) Lp spaces, using the usual square function defined by a dyadic partition.

We prove sharp weak and strong type weighted estimates for a class of dyadic operators that includes majorants of both standard singular integrals and square functions. Our main new result is the optimal bound…

In this article, we address endpoint issues for the bilinear spherical maximal functions. We obtain borderline restricted weak type estimates for the well studied bilinear spherical maximal function…

Almost everywhere convergence on the solution of Schr\"odinger equation is an important problem raised by Carleson in harmonic analysis. In recent years, this problem was essentially solved by building the sharp $L^p$-estimate of…

We give several sharp estimates for a class of combinations of second order Riesz transforms on Lie groups ${G}={G}_{x} \times {G}_{y}$ that are multiply connected, composed of a discrete abelian component ${G}_{x}$ and a connected…

We consider L^p two weight inequalities for maximal truncations of dyadic Calderon-Zygmund operators. In the case of one weight being doubling, a characterization is given, and for the general case, sufficient conditions are given,…

We obtain a generalization of the Two-Square Lemma proved for abelian categories by Fay, Hardie, and Hilton in 1989 and (in a special case) for preabelian categories by Generalov in 1994. We also prove the equivalence up to sign of two…

In the present paper, we consider the Cauchy problem of the system of quadratic derivative nonlinear Schr\"odinger equations for the spatial dimension $d=2$ and $3$. This system was introduced by M. Colin and T. Colin (2004). The first…