Keywords: Riesz potential; Sobolev's inequality; Orlicz-Morrey space; metric measure space; non-doubling measure
@article{10_21136_CMJ_2022_0149_22,
author = {Ohno, Takao and Shimomura, Tetsu},
title = {Riesz potentials and {Sobolev-type} inequalities in {Orlicz-Morrey} spaces of an integral form},
journal = {Czechoslovak Mathematical Journal},
pages = {263--276},
year = {2023},
volume = {73},
number = {1},
doi = {10.21136/CMJ.2022.0149-22},
mrnumber = {4541101},
zbl = {07655767},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2022.0149-22/}
}
TY - JOUR AU - Ohno, Takao AU - Shimomura, Tetsu TI - Riesz potentials and Sobolev-type inequalities in Orlicz-Morrey spaces of an integral form JO - Czechoslovak Mathematical Journal PY - 2023 SP - 263 EP - 276 VL - 73 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2022.0149-22/ DO - 10.21136/CMJ.2022.0149-22 LA - en ID - 10_21136_CMJ_2022_0149_22 ER -
%0 Journal Article %A Ohno, Takao %A Shimomura, Tetsu %T Riesz potentials and Sobolev-type inequalities in Orlicz-Morrey spaces of an integral form %J Czechoslovak Mathematical Journal %D 2023 %P 263-276 %V 73 %N 1 %U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2022.0149-22/ %R 10.21136/CMJ.2022.0149-22 %G en %F 10_21136_CMJ_2022_0149_22
Ohno, Takao; Shimomura, Tetsu. Riesz potentials and Sobolev-type inequalities in Orlicz-Morrey spaces of an integral form. Czechoslovak Mathematical Journal, Tome 73 (2023) no. 1, pp. 263-276. doi: 10.21136/CMJ.2022.0149-22
[1] Adams, D. R.: A note on Riesz potentials. Duke Math. J. 42 (1975), 765-778. | DOI | MR | JFM
[2] Björn, A., Björn, J.: Nonlinear Potential Theory on Metric Spaces. EMS Tracts in Mathematics 17. European Mathematical Society, Zürich (2011). | DOI | MR | JFM
[3] Burenkov, V. I., Guliyev, H. V.: Necessary and sufficient conditions for boundedness of the maximal operator in local Morrey-type spaces. Stud. Math. 163 (2004), 157-176. | DOI | MR | JFM
[4] Cruz-Uribe, D. V., Shukla, P.: The boundedness of fractional maximal operators on variable Lebesgue spaces over spaces of homogeneous type. Stud. Math. 242 (2018), 109-139. | DOI | MR | JFM
[5] Hajłasz, P., Koskela, P.: Sobolev met Poincaré. Mem. Am. Math. Soc. 688 (2000), 101 pages. | DOI | MR | JFM
[6] Hashimoto, D., Sawano, Y., Shimomura, T.: Gagliardo-Nirenberg inequality for generalized Riesz potentials of functions in Musielak-Orlicz spaces over quasi-metric measure spaces. Colloq. Math. 161 (2020), 51-66. | DOI | MR | JFM
[7] Hedberg, L. I.: On certain convolution inequalities. Proc. Am. Math. Soc. 36 (1972), 505-510. | DOI | MR | JFM
[8] Heinonen, J.: Lectures on Analysis on Metric Spaces. Universitext. Springer, New York (2001). | DOI | MR | JFM
[9] Hurri-Syrjänen, R., Ohno, T., Shimomura, T.: On Trudinger-type inequalities in Orlicz-Morrey spaces of an integral form. Can. Math. Bull. 64 (2021), 75-90. | DOI | MR | JFM
[10] Kairema, A.: Two-weight norm inequalities for potential type and maximal operators in a metric space. Publ. Mat., Barc. 57 (2013), 3-56. | DOI | MR | JFM
[11] Kairema, A.: Sharp weighted bounds for fractional integral operators in a space of homogeneous type. Math. Scand. 114 (2014), 226-253. | DOI | MR | JFM
[12] Maeda, F.-Y., Mizuta, Y., Ohno, T., Shimomura, T.: Boundedness of maximal operators and Sobolev's inequality on Musielak-Orlicz-Morrey spaces. Bull. Sci. Math. 137 (2013), 76-96. | DOI | MR | JFM
[13] Maeda, F.-Y., Ohno, T., Shimomura, T.: Boundedness of the maximal operator on Musielak-Orlicz-Morrey spaces. Tohoku Math. J. (2) 69 (2017), 483-495. | DOI | MR | JFM
[14] Mizuta, Y., Nakai, E., Ohno, T., Shimomura, T.: An elementary proof of Sobolev embeddings for Riesz potentials of functions in Morrey spaces $L^{1,\nu,\beta}(G)$. Hiroshima Math. J. 38 (2008), 425-436. | DOI | MR | JFM
[15] Mizuta, Y., Nakai, E., Ohno, T., Shimomura, T.: Boundedness of fractional integral operators on Morrey spaces and Sobolev embeddings for generalized Riesz potentials. J. Math. Soc. Japan 62 (2010), 707-744. | DOI | MR | JFM
[16] Mizuta, Y., Shimomura, T.: Continuity properties of Riesz potentials of Orlicz functions. Tohoku Math. J. (2) 61 (2009), 225-240. | DOI | MR | JFM
[17] Mizuta, Y., Shimomura, T.: Sobolev's inequality for Riesz potentials of functions in Morrey spaces of integral form. Math. Nachr. 283 (2010), 1336-1352. | DOI | MR | JFM
[18] 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 | JFM
[19] C. B. Morrey, Jr.: On the solutions of quasi-linear elliptic partial differential equations. Trans. Am. Math. Soc. 43 (1938), 126-166. | DOI | MR | JFM
[20] Nakai, E.: Hardy-Littlewood maximal operator, singular integral operators and the Riesz potentials on generalized Morrey spaces. Math. Nachr. 166 (1994), 95-103. | DOI | MR | JFM
[21] Nakai, E.: Generalized fractional integrals on Orlicz-Morrey spaces. Banach and Function Spaces Yokohama Publishers, Yokohama (2004), 323-333. | MR | JFM
[22] Nazarov, F., Treil, S., Volberg, A.: Cauchy integral and Calderón-Zygmund operators on nonhomogeneous spaces. Int. Math. Res. Not. 1997 (1997), 703-726. | DOI | MR | JFM
[23] Nazarov, F., Treil, S., Volberg, A.: Weak type estimates and Cotlar inequalities for Calderón-Zygmund operators on nonhomogeneous spaces. Int. Math. Res. Not. 1998 (1998), 463-487. | DOI | MR | JFM
[24] Ohno, T., Shimomura, T.: On Sobolev-type inequalities on Morrey spaces of an integral form. Taiwanese J. Math. 26 (2022), 831-845. | DOI | MR | JFM
[25] Peetre, J.: On the theory of $L_{p,\lambda}$ spaces. J. Funct. Anal. 4 (1969), 71-87. | DOI | MR | JFM
[26] Samko, N. G., Samko, S. G., Vakulov, B. G.: Weighted Sobolev theorem in Lebesgue spaces with variable exponent. J. Math. Anal. Appl. 335 (2007), 560-583. | DOI | MR | JFM
[27] Sawano, Y.: Sharp estimates of the modified Hardy-Littlewood maximal operator on the nonhomogeneous space via covering lemmas. Hokkaido Math. J. 34 (2005), 435-458. | DOI | MR | JFM
[28] Sawano, Y., Shigematsu, M., Shimomura, T.: Generalized Riesz potentials of functions in Morrey spaces $L^{(1,\varphi;\kappa)}(G)$ over non-doubling measure spaces. Forum Math. 32 (2020), 339-359. | DOI | MR | JFM
[29] Sawano, Y., Shimomura, T.: Sobolev embeddings for Riesz potentials of functions in non-doubling Morrey spaces of variable exponents. Collect. Math. 64 (2013), 313-350. | DOI | MR | JFM
[30] Sawano, Y., Shimomura, T.: Maximal operator on Orlicz spaces of two variable exponents over unbounded quasi-metric measure spaces. Proc. Am. Math. Soc. 147 (2019), 2877-2885. | DOI | MR | JFM
[31] Sawano, Y., Shimomura, T., Tanaka, H.: A remark on modified Morrey spaces on metric measure spaces. Hokkaido Math. J. 47 (2018), 1-15. | DOI | MR | JFM
[32] Serrin, J.: A remark on the Morrey potential. Control Methods in PDE-Dynamical Systems Contemporary Mathematics 426. AMS, Providence (2007), 307-315. | DOI | MR | JFM
[33] Sihwaningrum, I., Sawano, Y.: Weak and strong type estimates for fractional integral operators on Morrey spaces over metric measure spaces. Eurasian Math. J. 4 (2013), 76-81. | MR | JFM
[34] Stempak, K.: Examples of metric measure spaces related to modified Hardy-Littlewood maximal operators. Ann. Acad. Sci. Fenn., Math. 41 (2016), 313-314. | DOI | MR | JFM
[35] Strömberg, J.-O.: Weak type $L^1$ estimates for maximal functions on non-compact symmetric spaces. Ann. Math. (2) 114 (1981), 115-126. | DOI | MR | JFM
[36] Terasawa, Y.: Outer measures and weak type $(1,1)$ estimates of Hardy-Littlewood maximal operators. J. Inequal. Appl. 2006 (2006), Article ID 15063, 13 pages. | DOI | MR | JFM
Cité par Sources :