A note on choquet integrals with respect to Hausdorff capacity
A note on choquet integrals with respect to Hausdorff capacity
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DOI：
10.1007/bfb0078867
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发表时间：
1988
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影响因子：
--
通讯作者：
D. Adams
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文献类型：
--
作者：
D. Adams
其中上确界取于LR“中的ALI”坐标立方体上；UQ=U在Q上的积分平均值，1Q1表示Q的Lebesguen-测度。众所周知的H1-BMO对偶是BMO是H1·的对偶。我们还需要光滑稠密类S00=ALI1/>；E S，它是快速递减的C“”函数的Schwartz类，对于它，1/>的傅里叶变换与原点具有紧支集不交。M表示R“(局部有限正则符号Borel测度)上的”Radon测度“，M+(K)表示M中那些非负且在K中有支撑性的元素。L 1是指M中的全变差测度Ij，L 1=J.L++Jl-在R”上完全有限的元素。事实上，当没有混淆时，我们应该写iij。李为IJ。Li(Jr“)。L 1·d·O<；d：：；n是来自M的元素的Morrey空间，对M有lllţ。TLll=sup r-d Lţti(B(x，r))<；o.：z：；r>；0此外，Supp(JL)也用来表示对ţ的支持。符号“-”读作“是比较”，意思是有两个正的有限常量，使两个量的比率上下受这两个常量的限制；A-B IJF c 1A：：；B：：；C2a。字母c通常指的是与所述(或隐含的)变量无关的一般常量。
116 where the supremum is taken over ali" coordinate cubes" in lR"; UQ= integral avcrage of U over Q, and 1 Q 1 denotes the Lebesgue n-measure of Q. The well known H 1-BMO duality is that BMO is the dual of H 1• Also we need the smooth dense class S00= ali 1/> E S, the Schwartz class of rapidly decreasing C"" functions, for which the Fourier transform of 1/> has compact support disjoint from the origin. C0 (JR"), ego (R") are respectively, the continuous, the infinitely differentiable, functions with compact support on R". M denotes the" Radon measures" on R"(locally finite regular signed Borel measures), M+(K) refers to those elements of M that are non-negative and ha ve their support in K. L 1 are those elements of M for which the total variation measure IJ. L 1= J. L++ JL-is totally finite on R". In fact when there is no confusion, we shall write IIJ. Lih for IJ. Li (JR"). L 1· d· O< d::; n, is the Morrey space of elements from M for which lllţ. tlll= sup r-d lţti (B (x, r))< oo.: z:; r> 0Also, supp (JL) is used to denote the support of ţ. t. The symbol"-" is read" is compara bie to" and means that there are two positive finite constants such that the ratio of the two quantities under examination are bound above and below by these constants; A-B ijf c 1 A::; B::; c2 A. And the letter c will generally refer to a generic constant, independent of said (or implied) variables.