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1)  Dini condition
Dini条件
1.
Let {p_j}~m_(j=1) be positive continuous real-valued function on R~d,and {logp_j}~m_(j=1) satisfy the Dini condition.
设{pj}jm=1是Rd上的正连续函数,且{logpj}jm=1满足Dini条件
2.
Boundary regularity results for viscosity solutions of Poisson s equation and fully nonlinear uniformly elliptic equations under the Dini condition are obtained by use of Caffarelli s perturbation method, which give a simple proof of Theorem 4.
笔者利用Caffarelli扰动方法,证明了Poisson方程和完全非线性一致椭圆型方程在Dini条件下其粘性解的边界正则性,从而给出了文[8]定理4。
2)  Dini-condition
Dini条件
1.
the variable kernel is proved that if the kernel satisfies the Dini-condition, then the commutators with variable kernel are bounded from H K_(q,b)~(α,p)(R~n) into K_q~(α,p)(R~n) and its endpoint estimates are also established.
在第三章中,我们研究了一类带有变量核的积分算子和CBMO函数生成的交换子,当核函数满足一类Dini条件时在Herz型Hardy空间上的有界性。
3)  Dini-type condition
Dini条件
1.
In order to enlarge the research scope,the authors decline the condition of kernel to Dini-type condition;and by using the quality of kernel and technique estimation,the authors obtain some weighted norm inequalities for the singular integral operator with Dini-type condition.
研究了具有标准核的奇异积分算子,为了扩大奇异积分算子的研究范围,现将核的条件减弱成Dini条件,利用核的性质及一些技巧性估计,得到Dini型核奇异积分算子关于任意权函数的几个加权赋范不等式。
4)  Dini type condition
Dini型条件
1.
For the commutators of Multilinear Marcinkiewicz integral μΩ,A(f)(x),the endpoint estimates are obtained when function b(x)∈BMO,Ω satisfies the Dini type conditions.
得到了当函数b(x)∈BMO,Ω满足Dini型条件时多线性Marcinkiewicz积分交换子μΩ,A(f)(x)的端点估计。
2.
For the commutators μ_(Ω,b)(f) of Marcinkiewicz integrals with Ω satisfying the Dini type condition,it is shown that the following inequality holdsu({x∈R~n:μ_(Ω,b)(f)(x)>λ})≤CCt~p∫_(R~n)|f|~pvdx,where(u,v) satisfy(1|Q|∫_Qu~rdx)~(1/rp)‖v~(-1/p)‖_(c,Q)≤C<∞.
得到了Ω满足Dini型条件时Marcinkiewicz积分交换子μΩ,b(f)的双权弱型估计u({x∈Rn:μΩ,b(f)(x)>λ})≤CtC∫pRn|f|pvdx,其中(u,v)满足(|1Q|∫Qurdx)1/rp‖v-1/p‖c,Q≤C<∞。
5)  Dini-type condition
Dini型条件
1.
Estimation and application of kernel of singular integral operators with Dini-type condition;
具有Dini型条件的奇异积分算子的核的估计及应用
2.
It is proved that the Marcinkiewicz integralμΩis an operator of type (Hp,∞, Lp,∞) for 0 < p < I, hereΩis homogeneous of degree zero on Rn and satisfies a kind of Dini-type condition.
本文证明了Marcinkiewicz积分μΩ是(Hp,∞,Lp,∞)型的算子(0
3.
In the first chapter,we prove that the Marcinkiewicz integral op-eratorμΩis an operator of type(H~(p,∞),L~(p,∞))for(0<p<1),hereΩis homogeneous of degree zero on R~n satisfying a kind of Dini-type condition.
在第一章中,我们证明了Marcinkiewicz积分算子μΩ是(H~(p,∞),L~(p,∞))型的算子(0<p<1),这里Ω是满足一类Dini型条件的R~n上的零次齐次函数。
6)  L~q-Dini condition
Lq-Dini条件
1.
It is known that when a homogeneous function of degree zero satisfies L~q-Dini condition,the singular integral operator is bounded on L~p(1<p<∞).
我们知道,零次齐次函数Ω(x)满足Lq-Dini条件时,奇异积分算子T是Lp有界的,其中1
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分子式:
CAS号:

性质:又称4,8-二硝基蒽绛酚。从硝基苯中析出黄色结晶。熔点>330℃。稍溶于多数普通有机溶剂。易溶于碱。由1,5-二氯蒽醌经苯氧基化或甲氧基化,硝化和水解而得。也可由1,5-二羟基蒽醌硝化而得。主要用作分散和还原等染料的中间体。

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