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arXiv · 2101.07588

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

Boning Di·Qianjun He·Dunyan Yan
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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 $1\leq p\leq q<\infty$ under a condition of $(u,v)\in \bigcup_{b'>a} A_{p,q,\alpha}^{b'}$, 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 $(u,v)\in\mathscr{M}_{p,q,\alpha}^{6a+9\sqrt{d}a^2}$ and the two-weight strong-type boundedness of the local fractional integrals. These estimates are established by the radialization method and dyadic approach.

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Boning Di, Qianjun He, Dunyan Yan. 2021-01-19. Two-weight Norm Inequalities for Local Fractional Integrals on Gaussian Measure Spaces. https://doi.org/10.1007/s10114-022-1114-6

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