1) dini theorem
Dini定理
2) Dini kernel
Dini核
1.
To study that maximal singular integral operators with Dini kernels are from L~1 to L~(1,∞) and L~p bounded for 1<p<∞ if ∈A_p.
学习在非双倍测度的条件下,具有Dini核的极大奇异积分算子是从L1( ω)到L1,∞( ω)和Lp( ω)有界的,其中1
3) 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<∞。
4) 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。
6) 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。
补充资料：Dini定理
Dini定理
Dim theorem
肠亩定理【l芳亩U脚.n;几“Ho TeopeMa]，关于一致收效性的 如果函数气(。”l，2，…在区间[a，b]上是连续的、非负的，并且级数艺二:u，之和是Ia，b]上的连续函数，则此级数在[a，b]上一致收敛.D五lj定理可以推广到函数“，的定义域为任意紧统(compaCtum)的情况.
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参考词条