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Start Over Creator Hu, Guoen

1. A new characterization of ${\rm RBMO}(\mu )$ by John-Strömberg sharp maximal functions

Creator:
Hu, Guoen, Yang, Dachun, and Yang, Dongyong
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
non-doubling measure, $\mathop{\rm RBMO}(\mu )$, and sharp maximal function
Language:
English
Description:
Let $\mu $ be a nonnegative Radon measure on ${{\mathbb R}^d}$ which only satisfies $\mu (B(x, r))\le C_0r^n$ for all $x\in {{\mathbb R}^d}$, $r>0$, with some fixed constants $C_0>0$ and $n\in (0,d].$ In this paper, a new characterization for the space $\mathop{\rm RBMO}(\mu )$ of Tolsa in terms of the John-Strömberg sharp maximal function is established.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Estimates for the commutator of bilinear Fourier multiplier

Creator:
Hu, Guoen and Yi, Wentan
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
bilinear Fourier multiplier operator, commutator, and Hardy space
Language:
English
Description:
Let $b_1, b_2 \in {\rm BMO}(\mathbb {R}^n)$ and $T_{\sigma }$ be a bilinear Fourier multiplier operator with associated multiplier $\sigma $ satisfying the Sobolev regularity that $\sup _{\kappa \in \mathbb {Z}} \|\sigma _{\kappa }\| _{W^{s_1,s_2}(\mathbb {R}^{2n})}<\infty $ for some $s_1,s_2\in (n/2,n]$. In this paper, the behavior on $L^{p_1}(\mathbb {R}^n)\times L^{p_2}(\mathbb {R}^n)$ $(p_1,p_2\in (1,\infty ))$, on $H^1(\mathbb {R}^n)\times L^{p_2}(\mathbb {R}^n)$ $(p_2\in [2,\infty ))$, and on $H^1(\mathbb {R}^n)\times H^1(\mathbb {R}^n)$, is considered for the commutator $T_{{\sigma }, \vec {b}} $ defined by $$ \begin {aligned} T_{\sigma ,\vec {b}} (f_1,f_2) (x)=&b_1(x)T_{\sigma }(f_1, f_2)(x)-T_{\sigma }(b_1f_1, f_2)(x) &+ b_2(x)T_{\sigma }(f_1, f_2)(x)-T_{\sigma }(f_1, b_2f_2)(x) . \end {aligned} $$ By kernel estimates of the bilinear Fourier multiplier operators and employing some techniques in the theory of bilinear singular integral operators, it is proved that these mapping properties are very similar to those of the bilinear Fourier multiplier operator which were established by Miyachi and Tomita.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public