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pro vyhledávání: '"He, DanQing"'
We improve the range of indices when the multilinear Bochner-Riesz means converges pointwisely. We obtain this result by establishing the $L^p$ estimates and weighted estimates of $k$-linear maximal Bochner-Riesz operators inductively, which is new w
Externí odkaz:
http://arxiv.org/abs/2412.00296
For $p\ge 2$, and $\lambda>\max\{n|\tfrac 1p-\tfrac 12|-\tfrac12, 0\}$, we prove the pointwise convergence of cone multipliers, i.e. $$ \lim_{t\to\infty}T_t^\lambda(f)\to f \text{ a.e.},$$ where $f\in L^p(\mathbb R^n)$ satisfies $supp\ \widehat f\sub
Externí odkaz:
http://arxiv.org/abs/2405.02607
In this paper, we investigate the H\"ormander type theorems for the multi-linear and multi-parameter Fourier multipliers. When the multipliers are characterized by $L^u$-based Sobolev norms for $1
Externí odkaz:
http://arxiv.org/abs/2306.08462
We study $m$-linear homogeneous rough singular integral operators $\mathcal{L}_{\Omega}$ associated with integrable functions $\Omega$ on $\mathbb{S}^{mn-1}$ with mean value zero. We prove boundedness for $\mathcal{L}_{\Omega}$ from $L^{p_1}\times \c
Externí odkaz:
http://arxiv.org/abs/2207.00764
Autor:
He, Danqing, Park, Bae Jun
We study bilinear rough singular integral operators $\mathcal{L}_{\Omega}$ associated with a function $\Omega$ on the sphere $\mathbb{S}^{2n-1}$. In the recent work of Grafakos, He, and Slav\'ikov\'a (Math. Ann. 376: 431-455, 2020), they showed that
Externí odkaz:
http://arxiv.org/abs/2104.14137
In this work we obtain the pointwise almost everywhere convergence for two families of multilinear operators: (a) truncated homogeneous singular integral operators associated with $L^q$ functions on the sphere and (b) lacunary multiplier operators of
Externí odkaz:
http://arxiv.org/abs/2012.10837
The $L^p$ boundedness theory of convolution operators is \linebreak based on an initial $L^2\to L^2$ estimate derived from the Fourier transform. The corresponding theory of multilinear operators lacks such a simple initial estimate in view of the un
Externí odkaz:
http://arxiv.org/abs/2010.15312
Let $H = -\Delta + |x|^2$ be the Hermite operator in ${\mathbb R}^n$. In this paper we study almost everywhere convergence of the Bochner-Riesz means associated with $H$ which is defined by $S_R^{\lambda}(H)f(x) = \sum\limits_{k=0}^{\infty} \big(1-{2
Externí odkaz:
http://arxiv.org/abs/2006.05689
Autor:
He, Danqing, Shi, Zuoshunhua
We obtain sharp $L^p$ bounds for oscillatory integral operators with generic homogeneous polynomial phases in several variables. The phases considered in this paper satisfy the rank one condition which is an important notion introduced by Greenleaf,
Externí odkaz:
http://arxiv.org/abs/1905.07980
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