一类次线性算子在非双倍测度下的有界性(英文)

BOUNDEDNESS OF THE SUB-LINEAR OPERATORS FOR NON-DOUBLING MEASURE

本文研究了算子在d上只满足增长条件的Randon测度μ条件下的有界性问题,利用Lq有界性假设、Herz空间的概念和次线性算子的性质,证明了在非双倍测度下,一类次线性算子在Herz空间中的几个有界性.推广了双倍测度时的情形.

In this paper,we discuss the boundedness of operators under the growth condition on Randon measure μ on R^d which may be non-doubling.By the definition of the Herz spaces and the properties of the sublinear operator,we obtain some results on boundedness of the sub-linear operator on Herz spaces for non-doubling measure with L^q boundedness.And these results generalize the same conclusion for doubling measure.