In this paper we show that if K(x)=Ω(x)l|\x|~n is a Calderon-Zygmu- nd kernel,where Ω∈L^q(S^(n-1)) for some 1<q≤∞,and b(x) is a radial function such that |b(r)|~p·dr≤cR for all R>0 and some 1<p_0&...In this paper we show that if K(x)=Ω(x)l|\x|~n is a Calderon-Zygmu- nd kernel,where Ω∈L^q(S^(n-1)) for some 1<q≤∞,and b(x) is a radial function such that |b(r)|~p·dr≤cR for all R>0 and some 1<p_0<∞,then Tf=P.V.(bK)*f is bounded on L^p() for 1<p≤∞ and n≥2.Moreover, we show that T is bounded from BMO to BMO iff b(x) is satisfied the condition star (*).展开更多
Brouéand Puig set the definition of nilpotent p-blocks, stated the existence of such blocks, and then proved that there is a unique Brauer character in a nilpotent p-block. The present paper, based on the works o...Brouéand Puig set the definition of nilpotent p-blocks, stated the existence of such blocks, and then proved that there is a unique Brauer character in a nilpotent p-block. The present paper, based on the works of Slattery and Robinson, generalizes the above idea to theπ-block theory of aπ-separable group, defines the nilpotency of aπ-block, and proves that there is a unique B_(π')-character in a nilpotentπ-block.展开更多
Let π be a set of primes and G a π-separable group. Isaacs defines the Bπ characters, which can be viewed as the "π-modular" characters in G, such that the Bp′ characters form a set of canonical lifts f...Let π be a set of primes and G a π-separable group. Isaacs defines the Bπ characters, which can be viewed as the "π-modular" characters in G, such that the Bp′ characters form a set of canonical lifts for the p-modular characters. By using Isaacs' work, Slattery has developed some Brauer's ideals of p-blocks to the π-blocks of a finite π-separable group, generalizing Brauer's three main theorems to the π-blocks. In this paper, depending on Isaacs' and Slattery's work, we will extend the first main theorem for π-blocks.展开更多
The sympathetic nervous system is activated in the setting of heart failure(HF)to compensate for hemodynamic instability.However,acute sympathetic surge or sustained high neuronal firing rates activatesβ-adrenergic r...The sympathetic nervous system is activated in the setting of heart failure(HF)to compensate for hemodynamic instability.However,acute sympathetic surge or sustained high neuronal firing rates activatesβ-adrenergic receptor(βAR)signaling contributing to myocardial remodeling,dysfunction and electrical instability.Thus,sympathoβAR activation is regarded as a hallmark of HF and forms pathophysiological basis forβ-blocking therapy.Building upon earlier research findings,studies conducted in the recent decades have significantly advanced our understanding on the sympatho-adrenergic mechanism in HF,which forms the focus of this article.This review notes recent research progress regarding the roles of cardiacβ2AR orα1AR in the failing heart,significance ofβ1AR-autoantibodies,andβAR signaling through G-protein independent signaling pathways.Sympatho-βAR regulation of immune cells or fibroblasts is specifically discussed.On the neuronal aspects,knowledge is assembled on the remodeling of sympathetic nerves of the failing heart,regulation by presynapticα2AR of NE release,and findings on device-based neuromodulation of the sympathetic nervous system.The review ends with highlighting areas where significant knowledge gaps exist but hold promise for new breakthroughs.展开更多
文摘In this paper we show that if K(x)=Ω(x)l|\x|~n is a Calderon-Zygmu- nd kernel,where Ω∈L^q(S^(n-1)) for some 1<q≤∞,and b(x) is a radial function such that |b(r)|~p·dr≤cR for all R>0 and some 1<p_0<∞,then Tf=P.V.(bK)*f is bounded on L^p() for 1<p≤∞ and n≥2.Moreover, we show that T is bounded from BMO to BMO iff b(x) is satisfied the condition star (*).
基金This work was partially supported by the National Natural Science Foundation of China (Grant No. 10771132)Beijing Educational Committee (Grant No. Km200510028002)
文摘Brouéand Puig set the definition of nilpotent p-blocks, stated the existence of such blocks, and then proved that there is a unique Brauer character in a nilpotent p-block. The present paper, based on the works of Slattery and Robinson, generalizes the above idea to theπ-block theory of aπ-separable group, defines the nilpotency of aπ-block, and proves that there is a unique B_(π')-character in a nilpotentπ-block.
基金supported by the National Natural Science Foundation of China(Grant No.10471085)the BS Foundation of Shandong Province,China(Grant No.03bs006).
文摘Let π be a set of primes and G a π-separable group. Isaacs defines the Bπ characters, which can be viewed as the "π-modular" characters in G, such that the Bp′ characters form a set of canonical lifts for the p-modular characters. By using Isaacs' work, Slattery has developed some Brauer's ideals of p-blocks to the π-blocks of a finite π-separable group, generalizing Brauer's three main theorems to the π-blocks. In this paper, depending on Isaacs' and Slattery's work, we will extend the first main theorem for π-blocks.
基金funded by competitive fellowship or project grants from the National Health and Medical Research Council of Australia(236884,1032687,1043026,1081710)National Heart Foundation of Australia(G03M1126,G10M5126)the National Science Foundation of China(81870223,81870300).
文摘The sympathetic nervous system is activated in the setting of heart failure(HF)to compensate for hemodynamic instability.However,acute sympathetic surge or sustained high neuronal firing rates activatesβ-adrenergic receptor(βAR)signaling contributing to myocardial remodeling,dysfunction and electrical instability.Thus,sympathoβAR activation is regarded as a hallmark of HF and forms pathophysiological basis forβ-blocking therapy.Building upon earlier research findings,studies conducted in the recent decades have significantly advanced our understanding on the sympatho-adrenergic mechanism in HF,which forms the focus of this article.This review notes recent research progress regarding the roles of cardiacβ2AR orα1AR in the failing heart,significance ofβ1AR-autoantibodies,andβAR signaling through G-protein independent signaling pathways.Sympatho-βAR regulation of immune cells or fibroblasts is specifically discussed.On the neuronal aspects,knowledge is assembled on the remodeling of sympathetic nerves of the failing heart,regulation by presynapticα2AR of NE release,and findings on device-based neuromodulation of the sympathetic nervous system.The review ends with highlighting areas where significant knowledge gaps exist but hold promise for new breakthroughs.
