共查询到20条相似文献,搜索用时 23 毫秒
1.
In this paper, we define the Morrey spaces M_F~(p,q) (Rn) and the Campanato spaces E_F~(p,q) (R~n) associated with a family F of sections and a doubling measure μ, where F is closely related to the Monge-Amp`ere equation. Furthermore, we obtain the boundedness of the Hardy-Littlewood maximal function associated to F, Monge-Amp`ere singular integral operators and fractional integrals on M_F~(p,q)(R~n). We also prove that the Morrey spaces M_F~(p,q) (R~n)and the Campanato spaces E_F~(p,q) (R~n) are equivalent with 1 ≤ q ≤ p ∞. 相似文献
2.
Yongtao Jing & Zhaoli Liu 《数学研究》2015,48(3):290-305
Let $1
0.$ This is in sharp contrast to D'Aprile and Mugnai's non-existence results. 相似文献
3.
赵俊燕 《数学年刊A辑(中文版)》2017,38(4):405-418
研究了欧氏空间R~2中单位方体Q~2=[0,1]~2上沿曲面(t,s,γ(t,s))的振荡奇异积分算子T_(α,β)f(u,v,x)=∫_(Q~2)f(u-t,v-s,x-γ(t,s))e~(it~(-β_1)s~(-β_2))t~(-1-α_1)s~(-1-α_2)dtds从Sobolev空间L_τ~p(R~(2+n))到L~p(R~(2+n))中的有界性,其中x∈R~n,(u,v)∈R~2,(t,s,γ(t,s))=(t,s,t~(P_1)s~(q_1),t~(p_2)s~(q_2),…,t~(p_n)s~(q_n))为R~(2+n)上一个曲面,且β_1α_1≥0,β_2α_20.这些结果推广和改进了R~3上的某些已知的结果.作为应用,得到了乘积空间上粗糖核奇异积分算子的Sobolev有界性. 相似文献
4.
Potential Analysis - We obtain Littlewood-Paley formulas for Fock spaces ${\mathcal {F}}_{\beta ,\omega }^{q}$ induced by weights $\omega \in {A}_{\infty }^{restricted} = \cup _{1 \le p <... 相似文献
5.
In this paper, the authors give the local L~2 estimate of the maximal operator S_(φ,γ)~* of the operator family {S_(t,φ,γ)} defined initially by ■which is the solution(when n = 1) of the following dispersive equations(~*) along a curve γ:■where φ : R~+→R satisfies some suitable conditions and φ((-?)~(1/2)) is a pseudo-differential operator with symbol φ(|ξ|). As a consequence of the above result, the authors give the pointwise convergence of the solution(when n = 1) of the equation(~*) along curve γ.Moreover, a global L~2 estimate of the maximal operator S_(φ,γ)~* is also given in this paper. 相似文献
6.
We study the L p boundedness of the generalized Bochner–Riesz means S λ which are defined as $$S^{\lambda}f(x) = \mathcal{F}^{-1} \left[\left(1 - \rho \right)_{+}^{\lambda} \widehat{f} \right](x)$$ where ${\rho(\xi) = {\rm max}\{|\xi_{1}|, \ldots, |\xi_{\ell}|\}}$ for ${\xi = (\xi_{1},\ldots, \xi_{\ell}) \in \mathbb{R}^{{d}_{1}} \times \cdots \times \mathbb{R}^{{d}_{\ell}}}$ and ${\mathcal{F}^{-1}}$ is the inverse Fourier transform. 相似文献
7.
Liu Qiao 《Journal of Applied Analysis & Computation》2014,4(4):355-365
We provide two regularity criteria for the weak solutions of the 3D micropolar fluid equations, the first one in terms of one directional derivative of the velocity, i.e., $\partial_{3}u$, while the second one is is in terms of the behavior of the direction of the velocity $\frac{u}{|u|}$. More precisely, we prove that if \begin{equation*} \partial_{3}u \in L^{\beta}(0,T;L^{\alpha}(\mathbb{R}^{3}))\quad\text{ with }\frac{2}{\beta}+\frac{3}{\alpha}\leq 1+\frac{1}{\alpha}, 2< \alpha \leq\infty, 2\leq\beta< \infty; \end{equation*} or \begin{equation*} \operatorname{div}\left(\frac{u}{|u|}\right)\in L^{\frac{4}{1-2r}}(0,T;\dot{X}_{r}(\mathbb{R}^{3}))\quad \text{ with } 0\leq r< \frac{1}{2}, \end{equation*} then the weak solution $(u(x,t),\omega(x,t))$ is regular on $\mathbb{R}^{3}\times [0,T]$. Here $\dot{X}_{r}(\mathbb{R}^{3})$ is the multiplier space. 相似文献
8.
Let N denote the set of all nonnegative integers and A be a subset of N.Let W be a nonempty subset of N.Denote by F~*(W) the set of all finite,nonempty subsets of W.Fix integer g≥2,let A_g(W) be the set of all numbers of the form sum f∈Fa_fg~f where F∈F~*(W)and 1≤a_f≤g-1.For i=0,1,2,3,let W_i = {n∈N|n≡ i(mod 4)}.In this paper,we show that the set A = U_i~3=0 A_g(W_i) is a minimal asymptotic basis of order four. 相似文献
9.
Under the Keller?COsserman condition on ${\Sigma_{j=1}^{2}f_{j}}$ , we show the existence of entire positive solutions for the semilinear elliptic system ${\Delta u_{1}+|\nabla u_{1}|=p_{1}(x)f_{1}(u_{1},u_{2}), \Delta u_{2}+|\nabla u_{2}|=p_{2}(x)f_{2}(u_{1},u_{2}),x \in \mathbb{R}^{N}}$ , where ${p_{j}(j=1, 2):\mathbb{R}^{N} \rightarrow [0,\infty)}$ are continuous functions. 相似文献
10.
Nuria Corral Percy Ferná ndez-Sá nchez 《Proceedings of the American Mathematical Society》2006,134(4):1125-1132
We bound the equisingularity type of the set of isolated separatrices of a holomorphic foliation of in terms of the Milnor number of . This result gives a bound for the degree of an algebraic invariant curve of a foliation of in terms of the degree of , provided that all the branches of are isolated separatrices.
11.
On the real line, the Dunkl operators$$D_{\nu}(f)(x):=\frac{d f(x)}{dx} + (2\nu+1) \frac{f(x) - f(-x)}{2x}, ~~ \quad\forall \, x \in \mathbb{R}, ~ \forall \, \nu \ge -\tfrac{1}{2}$$are differential-difference operators associated with the reflection group $\mathbb{Z}_2$ on $\mathbb{R}$, and on the $\mathbb{R}^d$ the Dunkl operators $\big\{D_{k,j}\big\}_{j=1}^{d}$ are the differential-difference operators associated with the reflection group $\mathbb{Z}_2^d$ on $\mathbb{R}^{d}$.In this paper, in the setting $\mathbb{R}$ we show that $b \in BMO(\mathbb{R},dm_{\nu})$ if and only if the maximal commutator $M_{b,\nu}$ is bounded on Orlicz spaces $L_{\Phi}(\mathbb{R},dm_{\nu})$. Also in the setting $\mathbb{R}^{d}$ we show that $b \in BMO(\mathbb{R}^{d},h_{k}^{2}(x) dx)$ if and only if the maximal commutator $M_{b,k}$ is bounded on Orlicz spaces $L_{\Phi}(\mathbb{R}^{d},h_{k}^{2}(x) dx)$. 相似文献
12.
13.
Sadek Gala 《NoDEA : Nonlinear Differential Equations and Applications》2010,17(2):181-194
In this paper, some improved regularity criteria for the 3D magneto-micropolar fluid equations are established in Morrey–Campanato
spaces. It is proved that if the velocity field satisfies
$\quad u\in L^{\frac{2}{1-r}}\left(0,T;\overset{.}{\mathcal{M}}_{p,\frac{3}{r}}( \mathbb{R}^{3})\right)\quad\text{with}
\;r\in \left( 0,1\right)\;\text{or}\;u\in C\left(0,T;\overset{.}{\mathcal{M}}_{p,\frac{3}{r}}(\mathbb{R} ^{3})\right)$\quad u\in L^{\frac{2}{1-r}}\left(0,T;\overset{.}{\mathcal{M}}_{p,\frac{3}{r}}( \mathbb{R}^{3})\right)\quad\text{with}
\;r\in \left( 0,1\right)\;\text{or}\;u\in C\left(0,T;\overset{.}{\mathcal{M}}_{p,\frac{3}{r}}(\mathbb{R} ^{3})\right) 相似文献
14.
In this paper we investigate symmetry results for positive solutions of systems involving the fractional Laplacian
15.
Kyriakos Keremedis 《Mathematical Logic Quarterly》2012,58(3):130-138
Given a set X, $\mathsf {AC}^{\mathrm{fin}(X)}$ denotes the statement: “$[X]^{<\omega }\backslash \lbrace \varnothing \rbrace$ has a choice set” and $\mathcal {C}_\mathrm{R}\big (\mathbf {2}^{X}\big )$ denotes the family of all closed subsets of the topological space $\mathbf {2}^{X}$ whose definition depends on a finite subset of X. We study the interrelations between the statements $\mathsf {AC}^{\mathrm{fin}(X)},$ $\mathsf {AC}^{\mathrm{fin}([X]^{<\omega })},$ $\mathsf {AC}^{\mathrm{fin} (F_{n}(X,2))},$ $\mathsf {AC}^{\mathrm{fin}(\mathcal {\wp }(X))}$ and “$\mathcal {C}_\mathrm{R}\big (\mathbf {2}^{X}\big )\backslash \lbrace \varnothing \rbrace$has a choice set”. We show:
16.
Krzysztof Plotka 《Proceedings of the American Mathematical Society》2003,131(4):1031-1041
We say that a function is a Hamel function ( ) if , considered as a subset of , is a Hamel basis for . We prove that every function from into can be represented as a pointwise sum of two Hamel functions. The latter is equivalent to the statement: for all there is a such that . We show that this fails for infinitely many functions.
17.
假设a,b0并且K_(a,b)(x)=(e~(i|x|~(-b)))/(|x|~(n+a))定义强奇异卷积算子T如下:Tf(x)=(K_(a,b)*f)(x),本文主要考虑了如上定义的算子T在Wiener共合空间W(FL~p,L~q)(R~n)上的有界性.另一方面,设α,β0并且γ(t)=|t|~k或γ(t)=sgn(t)|t|~k.利用振荡积分估计,本文还研究了算子T_(α,β)f(x,y)=p.v∫_(-1)~1f(x-t,y-γ(t))(e~(2πi|t|~(-β)))/(t|t|~α)dt及其推广形式∧_(α,β)f(x,y,z)=∫_(Q~2)f(x-t,y-s,z-t~ks~j)e~(-2πit)~(-β_1_s-β_2)t~(-α_1-1)s~(-α_2-1)dtds在Wiener共合空间W(FL~p,L~q)上的映射性质.本文的结论足以表明,Wiener共合空间是Lebesgue空间的一个很好的替代. 相似文献
18.
Jan Kolá r Jan Kristensen 《Proceedings of the American Mathematical Society》2005,133(6):1699-1706
For a -smooth bump function we show that the gradient range is the closure of its interior, provided that admits a modulus of continuity satisfying as . The result is a consequence of a more general result about gradient ranges of bump functions of the same degree of smoothness. For such bump functions we show that for open sets , either the intersection is empty or its topological dimension is at least two. The proof relies on a new Morse-Sard type result where the smoothness hypothesis is independent of the dimension of the space.
19.
The Ces\aro operator $\mathcal{C}_{\alpha}$ is defined by \begin{equation*} (\mathcal{C}_{\alpha}f)(x) = \int_{0}^{1}t^{-1}f\left( t^{-1}x \right)\alpha (1-t)^{\alpha -1}\,dt~, \end{equation*} where $f$ denotes a function on $\mathbb{R}$. We prove that $\mathcal{C}_{\alpha}$, $\alpha >0$, is a bounded operator in the Hardy space $H^{p}$ for every $0 < p \leqq 1$. 相似文献
20.
考虑一类平坦凸曲线的Hilbert变换■.对于平坦凸曲线,给出H_γ是L~2有界的一些必要条件. 相似文献
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