Adam Nowak, Peter Sjögren
We investigate in detail the mapping properties of the maximal operator associated with the heat-diffusion semigroup corresponding to expansions with respect to multi-dimensional standard Laguerre functions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
$L^p$-boundedness properties for the maximal operators for semigroups associated with Bessel and Laguerre operators
本文证明了与 Bessel 和 Laguerre 算子的热半群相关的广义极大算子具有弱型 (1,1) 性质，该结果不仅涵盖已知结论，且证明方法更为简单。
Classical settings of discrete and continuous orthogonal expansions, like Laguerre, Bessel and Jacobi, are associated with second order differential operators playing the role of the Laplacian. These depend on certain parameters of type that are usually restricted to a half-line, or a product of half-lines if higher dimensions are considered. Following earlier research done by Hajmirzaahmad, we deal in this paper with Laplacians in the above-mentioned contexts with no restrictions on the type parameters and bring to attention naturally associated orthogonal systems that in fact involve the cla…
We study several fundamental harmonic analysis operators in the multi-dimensional context of the Dunkl harmonic oscillator and the underlying group of reflections isomorphic to $\mathbb{Z}_2^d$. Noteworthy, we admit negative values of the multiplicity functions. Our investigations include maximal operators, $g$-functions, Lusin area integrals, Riesz transforms and multipliers of Laplace and Laplace-Stieltjes type. By means of the general Calderón-Zygmund theory we prove that these operators are bounded on weighted $L^p$ spaces, $1 < p < \infty$, and from weighted $L^1$ to weighted weak $L^1$. …
We develop a technique of proving standard estimates in the setting of Laguerre function expansions of convolution type, which works for all admissible type multi-indices $α$ in this context. This generalizes a simpler method existing in the literature, but being valid for a restricted range of $α$. As an application, we prove that several fundamental operators in harmonic analysis of the Laguerre expansions, including maximal operators related to the heat and Poisson semigroups, Riesz transforms, Littlewood-Paley-Stein type square functions and multipliers of Laplace and Laplace-Stieltjes tra…
In this paper we give sufficient conditions on a measurable function $p:(0,\infty)^n\rightarrow [1,\infty)$ in order that harmonic analysis operators (maximal operators, Riesz transforms, Littlewood--Paley functions and multipliers) associated with $α$-Laguerre polynomial expansions are bounded on the variable Lebesgue space $L^{p(\cdot)} ((0,\infty)^n, μ_α)$, where $dμ_α(x)=2^n\prod_{j=1}^n \frac{x_j^{2α_j+1} e^{-x_j^2}}{Γ(α_j+1)} dx$, being $α=(α_1, \dots, α_n)\in [0,\infty)^n$ and $x=(x_1,\dots,x_n)\in (0,\infty)^n$.
Let X be an analytic vector field defined in a neighborhood of the origin of R^3, and let I be an analytically non-oscillatory integral pencil of X; that is, I is a maximal family of analytically non-oscillatory trajectories of X at the origin all sharing the same iterated tangents. We prove that if I is interlaced, then for any trajectory T in I, the expansion of the structure generated over the real field by T and all globally subanalytic sets is model-complete, o-minimal and polynomially bounded.
In this paper we give a criterion to prove boundedness results for several operators from $H^1((0,\infty),γ_α)$ to $L^1((0,\infty),γ_α)$ and also from $L^\infty((0,\infty),γ_α)$ to $\BMO((0,\infty),γ_α)$, with respect to the probability measure $dγ_α(x)=\frac{2}{Γ(α+1)} x^{2α+1} e^{-x^2} dx$ on $(0,\infty)$ when ${α>-\frac12}$. We shall apply it to establish endpoint estimates for Riesz transforms, maximal operators, Littlewood-Paley functions, multipliers of Laplace transform type, fractional integrals and variation operators in the Laguerre setting.
UMD Banach spaces and the maximal regularity for the square root of several operators
本文证明了与Hermite、Bessel或Laguerre型算子平方根相关的Cauchy问题的极大$L^p$-正则性可刻画Banach空间$X$的UMD性质。
Weighted norm inequalities of some singular integrals associated with Laguerre expansions
本文对拉盖尔算子$\mathcal L_ν$相关的奇异积分（含极大函数、里斯变换和平方函数）进行加权估计研究，完成了里斯变换在$ν\in (-1,\infty)^n$全范围的刻画，显著改进了已有文献结果。
Fourier series in orthogonal polynomials with respect to a measure $ν$ on $[-1,1]$ are studied when $ν$ is a linear combination of a generalized Jacobi weight and finitely many Dirac deltas in $[-1,1]$. We prove some weighted norm inequalities for the partial sum operators $S_n$, their maximal operator $S^*$ and the commutator $[M_b, S_n]$, where $M_b$ denotes the operator of pointwise multiplication by $b \in \BMO$. We also prove some norm inequalities for $S_n$ when $ν$ is a sum of a Laguerre weight on $\R^+$ and a positive mass on $0$.
We set out to build a framework for self-adjoint extension theory for powers of the Jacobi differential operator that does not make use of classical deficiency elements. Instead, we rely on simpler functions that capture the impact of these elements on extensions but are defined by boundary asymptotics. This new perspective makes calculations much more accessible and allows for a more nuanced analysis of the associated domains. The maximal domain for $n$-th composition of the Jacobi operator is characterized in terms of a smoothness condition for each derivative, and the endpoint behavior of f…
On $L^p$ norms of maximal operators
本文确定了多种极大算子的精确 $L^p$ 范数为 $p'$，涵盖热、Poisson 等半群及 Hardy–Littlewood 算子，并证明高维情形范数严格大于 $p'$。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。