Two-weight Norm Inequalities for Local Fractional Integrals on Gaussian Measure Spaces

Abstract

In this paper, the authors establish the two-weight boundedness of the local fractional maximal operators and local fractional integrals on Gaussian measure spaces associated with the local weights. More precisely, the authors first obtain the two-weight weak-type estimate for the local-$a$ fractional maximal operators of order $\alpha$ from $L^p(v)$ to $L^{q,\infty }(u)$ with $1\le p\le q<\infty$ under a condition of $(u,v)\in {\bigcup }_{b^{\prime }>a}{A}_{p,q,\alpha }^{b^{\prime }}$, and then obtain the two-weight weak-type estimate for the local fractional integrals. In addition, the authors obtain the two-weight strong-type boundedness of the local fractional maximal operators under a condition of $(u,v)\in {\mathcal{M}}_{p,q,\alpha }^{6a+9\sqrt{d}{a}^2}$ and the two-weight strong-type boundedness of the local fractional integrals. These estimates are established by the radialization method and dyadic approach.

arXiv comment25 pages, 2 figures

References in corpus (1)

• Some Weighted Estimates on Gaussian Measure Spaces