简介:Inthisnote,wedefineanewkindofspacesTFofTriebel-LizorkintypeandcharacterizeitviasequencespacelpAlsoaFouriermultipliertheoremisestablishedinthisnewspacesTFpaq
简介:在在形式e~(i|x|~a)的摆动的单个不可分的操作员T的Triebel-Lizorkin空格的围住的海角Ω(x)|x|~(-n)被学习∈R,≠0,1并且Ω∈L~1(S~(n-1))度零是同类的并且满足某些取消条件。什么时候内核Ω(x′)∈Llog~+L(S~(n-1)),F_p~(一,q)(R~n)围住上述操作符的海角被获得。同时,什么时候Ω(x)满足L~1-Dini状况,上述操作符T被围住onF_1~(0,1)(R~n)。
简介:LethbeameasurablefunctiondefinedonR+×R+.LetΩ∈L(logL+)νq(Sn1-1×Sn2-1)(1≤νq≤2)behomogeneousofdegreezeroandsatisfycertaincancellationconditions.WeshowthatthesingularintegralTf(x1,x2)=p.v.∫Rn1+n2Ω(y′1,y′2)h(|y1|,|y2|)|y1|n1|y2|n2f(x1-y1,x2-y2)dy1dy2mapsfromSα1,α2p,q˙F(Rn1×Rn2)boundedlytoitselffor1
简介:让b=(b_1,···,b_m),b_i∈Λ_(β_i)(R~n),1≤i≤m,0<β_i<β,0<β<1,[b,T]f(x)=∫_(R~n)(K是aCalderon-Zygmund的b_1(x)-b_1(y))···(b_m(x)-b_m(y))K(x-y)f(y)dy,核。在这篇论文,我们显示出那[b,T]从L~p(R~n)toF_p~被围住(β,∞)(R~n),以及[b,从L~p(R~n)的I_α]到F_q~(β,∞)(R~n),在哪儿1/q=1/p-α/n。