Related papers: $\mathbf{L}^p$-boundedness of the Bochner-Riesz op…

In this article, we investigate the boundedness of the bilinear Bochner-Riesz means $S^{\alpha }$ in the non-Banach triangle case. We improve the corresponding results in [Bern] in two aspects: Our partition of the non-Banach triangle is…

Let H be the Hermite operator -\Delta +|x|^2 on \mathbb{R}^n. We prove a weighted L^2 estimate of the maximal commutator operator \sup_{R>0}|[b, S_R^\lambda(H)](f)|, where [b, S_R^\lambda(H)](f) = bS_R^\lambda(H) f - S_R^\lambda(H)(bf) is…

We consider the following question: Are there exponents $2<p<q$ such that the Riesz projection is bounded from $L^q$ to $L^p$ on the infinite polytorus? We are unable to answer the question, but our counter-example improves a result of…

Peral/Miyachi's celebrated theorem on fixed time $L^{p}$ estimates with loss of derivatives for the wave equation states that the operator $(I-\Delta)^{- \frac{\alpha}{2}}\exp(i \sqrt{-\Delta})$ is bounded on $L^{p}(\mathbb{R}^{d})$ if and…

Let $M$ be a complete non-compact Riemannian manifold satisfying the doubling volume property as well as a Gaussian upper bound for the corresponding heat kernel. We study the boundedness of the Riesz transform $d\Delta ^{-\frac{1}{2}}$ on…

We study the $L^p$ regularity of the Bergman projection $P$ over the symmetrized polydisc in $\mathbb C^n$. We give a decomposition of the Bergman projection on the polydisc and obtain an operator equivalent to the Bergman projection over…

The $L^p$-boundedness for $p>2$ of the covariant Riesz transform on differential forms is proved for a class of non-compact weighted Riemannian manifolds under certain curvature and volume growth conditions, which in particular settles a…

For $ 0< \lambda < \frac{1}2$, let $ B_{\lambda }$ be the Bochner-Riesz multiplier of index $ \lambda $ on the plane. Associated to this multiplier is the critical index $1 < p_\lambda = \frac{4} {3+2 \lambda } < \frac{4}3$. We prove a…

The goal of this paper is to study the Riesz transforms $\na A^{-1/2}$ where $A$ is the Schr\"odinger operator $-\D-V, V\ge 0$, under different conditions on the potential $V$. We prove that if $V$ is strongly subcritical, $\na A^{-1/2}$ is…

Consider the space $\mathbb{R}_+^d=(0,\infty)^d$ equipped with Euclidean distance and the Lebesgue measure. For every $\alpha=(\alpha_1,...,\alpha_d)\in[-1/2,\infty)^d$, we consider the Hermite-Laguerre operator…

In this paper we introduce Stein's square function associated with bilinear Bochner-Riesz means and investigate its $L^p$ boundedness properties. Further, we discuss several applications of the square function in the context of bilinear…

In this paper we consider the wave operators $W_{\pm}$ for a Schr\"odinger operator $H$ in ${\bf{R}}^n$ with $n\geq 4$ even and we discuss the $L^p$ boundedness of $W_{\pm}$ assuming a suitable decay at infinity of the potential $V$. The…

We prove the $L^p$-boundedness, $1<p<\infty$, of the Polynomial Carleson operator in general dimension. This follows the author's resolution of the one dimensional case as well as the work of Zorin-Kranich on the higher dimensional case in…

We generalize the recent result of Erdo{\u g}an, Goldberg and Green on the $L^p$-boundedness of wave operators for two dimensional Schr\"odinger operators and prove that they are bounded in $L^p(\R^2)$ for all $1<p<\infty$ if and only if…

We present new results on the two-weighted boundedness of singular integral operators and $L^p$ boundedness of the Orlicz maximal function. Namely, we extend a theorem of P\'erez regarding the necessary and sufficient conditions for the…

In [Math. Ineq. \& appl., Vol 26 (2) (2023), 511-530] and [Period. Math. Hung., 89 (1) (2024), 116-128], the present author proved that the Riesz potential $I_{\alpha}$ extends to a bounded operator $H^{p(\cdot)}_{\omega}(\mathbb{R}^n) \to…

In this paper we study maximal and square functions associated with bilinear Bochner-Riesz means at the critical index. In particular, we prove that they satisfy weighted estimates from $L^{p_1}(w_1)\times L^{p_2}(w_2)\rightarrow L^p(v_w)$…

Let $L=-\sum_{i,j=1}^n a_{ij}D_iD_j$ be the elliptic operator in non-divergence form with smooth real coefficients satisfying uniformly elliptic condition. Let $W$ be the global nonnegative adjoint solution. If $W\in A_2$, we prove that the…

We give a simple proof of L^p boundedness of iterated commutators of Riesz transforms and a product BMO function. We use a representation of the Riesz transforms by means of simple dyadic operators - dyadic shifts - which in turn reduces…

We consider abstract non-negative self-adjoint operators on $L^2(X)$ which satisfy the finite speed propagation property for the corresponding wave equation. For such operators we introduce a restriction type condition which in the case of…