L^p-summability of Riesz means for the sublaplacian on complex spheres

Weighted restriction type estimates for grushin operators and application to spectral multipliers and bochner-riesz summability

We prove weighted restriction type estimates for Grushin operators. These estimates are then used to prove sharp spectral multiplier theorems as well as Bochner-Riesz summability results with sharp exponent.

生成有限阶全纯函数的Dirichlet级数的Riesz可和性

Riesz summability of Dirichlet series generating holomorphic functions of finite order

研究频率λ下生成有限阶全纯函数的λ-Dirichlet级数的Riesz可和性，提出新的分离条件，将Bohr定理从k=0推广到任意k≥0，并改进Defant和Schoolmann在Landau条件下的结果。

Bilinear Riesz means on the Heisenberg group

In this article, we investigate the bilinear Riesz means $S^{α}$ associated to the sublaplacian on the Heisenberg group. We prove that the operator $S^{α}$ is bounded from $L^{p_{1}}\times L^{p_{2}}$ into $ L^{p}$ for $1\leq p_{1}, p_{2}\leq \infty $ and $1/p=1/p_{1}+1/p_{2}$ when $ α$ is large than a suitable smoothness index $α(p_{1},p_{2})$. There are some essential differences between the Euclidean space and the Heisenberg group for studying the bilinear Riesz means problem. We make use of some special techniques to obtain a lower index $α(p_{1},p_{2})$.

Maximal estimates for the bilinear Riesz means on Heisenberg groups

In this article, we investigate the maximal bilinear Riesz means $S^{α}_{*}$ associated to the sublaplacian on the Heisenberg group. We prove that the operator $S^{α}_{*}$ is bounded from $L^{p_{1}}\times L^{p_{2}}$ into $% L^{p}$ for $2\leq p_{1}, p_{2}\leq \infty $ and $1/p=1/p_{1}+1/p_{2}$ when $% α$ is large than a suitable smoothness index $α(p_{1},p_{2})$. For obtaining a lower index $α(p_{1},p_{2})$, we define two important auxiliary operators and investigate their $L^{p}$ estimates,which play a key role in our proof.

About summability of Fourier-Laplace series

In this paper we study the almost everywhere convergence of the expansions related to the self-adjoint extension of the Laplace operator. The sufficient conditions for summability is obtained. For the orders of Riesz means, which greater than critical index $\frac{N-1}{2}$ we established the estimation for maximal operator of the Riesz means. Note that when order $α$ of Riesz means is less than critical index then for establish of the almost everywhere convergence requests to use other methods form proving negative results. We have constructed different method of summability of Laplace series,…

Riesz summability on boundary lines of holomorphic functions generated by Dirichlet series

A particular consequence of the famous Carleson-Hunt theorem is that the Taylor series expansions of bounded holomorphic functions on the open unit disk converge almost everywhere on the boundary, whereas on single points the convergence may fail. In contrast, Bayart, Konyagin, and Queffélec constructed an example of an ordinary Dirichlet series $\sum a_n n^{-s}$, which on the open right half-plane $[Re >0]$ converges pointwise to a bounded, holomorphic function -- but diverges at each point of the imaginary line, although its limit function extends continuously to the closed right half plane.…