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Keywords:
fractional integral operator; quasi-metric measure space; Hausdorff content; weak Choquet space; Ahlfors regular
fractional integral operator; quasi-metric measure space; Hausdorff content; weak Choquet space; Ahlfors regular
Summary:
We prove the boundedness of the generalized fractional maximal operator $M_{\alpha }$ and the generalized fractional integral operator $I_{\alpha }$ on weak Choquet spaces with respect to Hausdorff content over quasi-metric measure spaces.
References:
[1] Adams, D. R.: A note on Choquet integrals with respect to Hausdorff capacity. Function Spaces and Applications Lecture Notes in Mathematics 1302. Springer, Berlin (1988), 115-124. DOI 10.1007/BFb0078867 | MR 0942261 | Zbl 0658.31009
[2] Adams, D. R.: Choquet integrals in potential theory. Publ. Mat., Barc. 42 (1998), 3-66. DOI 10.5565/PUBLMAT_42198_01 | MR 1628134 | Zbl 0923.31006
[3] Björn, A., Björn, J.: Nonlinear Potential Theory on Metric Spaces. EMS Tracts in Mathematics 17. EMS Press, Zürich (2011). DOI 10.4171/099 | MR 2867756 | Zbl 1231.31001
[4] Hajłasz, P., Koskela, P.: Sobolev met Poincaré. Mem. Am. Math. Soc. 145 (2000), 101 pages. DOI 10.1090/memo/0688 | MR 1683160 | Zbl 0954.46022
[5] Hatano, N., Kawasumi, R., Saito, H., Tanaka, H.: Choquet integrals, Hausdorff content and fractional operators. (to appear) in Bull. Aust. Math. Soc. DOI 10.1017/S000497272400011X | MR 4803163
[6] Hedberg, L. I.: On certain convolution inequalities. Proc. Am. Math. Soc. 36 (1972), 505-510. DOI 10.1090/S0002-9939-1972-0312232-4 | MR 0312232 | Zbl 0283.26003
[7] Heinonen, J.: Lectures on Analysis on Metric Spaces. Universitext. Springer, New York (2001). DOI 10.1007/978-1-4613-0131-8 | MR 1800917 | Zbl 0985.46008
[8] Kairema, A.: Two-weight norm inequalities for potential type and maximal operators in a metric space. Publ. Mat., Barc. 57 (2013), 3-56. DOI 10.5565/PUBLMAT_57113_01 | MR 3058926 | Zbl 1284.42055
[9] Mizuta, Y., Shimomura, T., Sobukawa, T.: Sobolev's inequality for Riesz potentials of functions in non-doubling Morrey spaces. Osaka J. Math. 46 (2009), 255-271. MR 2531149 | Zbl 1186.31003
[10] Orobitg, J., Verdera, J.: Choquet integrals, Hausdorff content and the Hardy-Littlewood maximal operator. Bull. Lond. Math. Soc. 30 (1998), 145-150. DOI 10.1112/S0024609397003688 | MR 1489325 | Zbl 0921.42016
[11] Sawano, Y., Shimomura, T.: Fractional maximal operator on Musielak-Orlicz spaces over unbounded quasi-metric measure spaces. Result. Math. 76 (2021), Article ID 188, 22 pages. DOI 10.1007/s00025-021-01490-7 | MR 4305494 | Zbl 1479.42055
[12] Watanabe, H.: Estimates of fractional maximal functions in a quasi-metric space. Nat. Sci. Rep. Ochanomizu Univ. 56 (2006), 21-31. MR 2214968 | Zbl 1113.42018
[13] Watanabe, H.: Estimates of maximal functions by Hausdorff contents in a metric space. Potential Theory in Matsue Advanced Studies in Pure Mathematics 44. Mathematical Society of Japan, Tokyo (2006), 377-389. DOI 10.2969/aspm/04410377 | MR 2279770 | Zbl 1125.42008
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