The Kolmogorov–Riesz theorem and some compactness criterions of bounded subsets in weighted variable exponent amalgam and Sobolev spaces

• Autores: Ismail Aydın, Cihan Unal
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 71, Fasc. 3, 2020, págs. 349-367
• Idioma: inglés
• DOI: 10.1007/s13348-019-00262-5
• Texto completo no disponible (Saber más ...)
• Referencias bibliográficas
  • Aydın, I.: On variable exponent amalgam spaces. An. Ştiin ţ. Univ. “Ovidius” Constanţa Ser. Mat. 20(3), 5–20 (2012)
  • Aydın, I.: Weighted variable Sobolev spaces and capacity. J. Funct. Spaces Appl. (2012). https://doi.org/10.1155/2012/132690
  • Aydın, I.: On vector-valued classical and variable exponent amalgam spaces. Commun. Fac. Sci. Univ. Ank. Series A1 66(2), 100–114 (2017)
  • Aydın, I., Gurkanli, A.T.: Weighted variable exponent amalgam spaces $$W\left( L^{p(x)}, L_{w}^{q}\right) $$. Glas. Mat. 47(67), 165–174 (2012)
  • Bandaliyev, R.: Compactness criteria in weighted variable Lebesgue spaces. Miskolc Math. Notes 18(1), 95–101 (2017)
  • Bandaliyev, R., Górka, P.: Relatively compact sets in variable-exponent Lebesgue spaces. Banach J. Math. Anal. 12(2), 331–346 (2018)
  • Diening, L., Hästö, P.: Muckenhoupt weights in variable exponent spaces (preprint)
  • Duoandikoetxea, J.: Fourier Analysis. Graduate Studies in Mathematics 29. American Mathematical Society, Providence (2000)
  • Feichtinger, H.G.: A compactness criterion for translation invariant Banach spaces of functions. Anal. Math. 8, 165–172 (1982)
  • Fournier, J.J., Stewart, J.: Amalgams of $$L^{p}$$ and $$l^{q}$$. Bull. Am. Math. Soc. 13, 1–21 (1985)
  • Goes, S., Welland, R.: Compactness criteria for Köthe spaces. Math. Ann. 188, 251–269 (1970)
  • Górka, P., Macios, A.: The Riesz-Kolmogorov theorem on metric spaces. Miskolc Math. Notes 15(2), 459–465 (2014)
  • Górka, P., Macios, A.: Almost everything you need to know about relatively compact sets in variable Lebesgue spaces. J. Funct. Anal. 269(7),...
  • Górka, P., Rafeiro, H.: From Arzelà–Askoli to Riesz–Kolmogorov. Nonlinear Anal. 144, 23–31 (2016)
  • Grubb, G.: Distributions and Operators. Springer, New York (2009)
  • Gurkanli, A.T.: The amalgam spaces $$W(L^{p(x)};L^{\left\lbrace p_{n}\right\rbrace })$$ and boundedness of Hardy-Littlewood maximal operators....
  • Gurkanli, A.T., Aydın, I.: On the weighted variable exponent amalgam space $$W(L^{p(x)};L_{m}^{q})$$. Acta Math. Sci. 34(4), 1098–1110 (2014)
  • Hanche-Olsen, H., Holden, H.: The Kolmogorov–Riesz compactness theorem. Expo. Math. 28(4), 385–394 (2010)
  • Hanche-Olsen, H., Holden, H.: Addendum to “The Kolmogorov–Riesz compactness theorem” [Expo. Math. 28 (2010) 385–394]. Expo. Math. 34, 243–245...
  • Hanche-Olsen, H., Holden, H., Malinnikova, E.: An improvement of the Kolmogorov–Riesz compactness theorem. Expo. Math. 37, 84–91 (2019)
  • Heinonen, J.: Lectures on Analysis on Metric Spaces. Universitext (2001)
  • Holland, F.: Harmonic analysis on amalgams of $$L^{p}$$ and $$l^{q}$$. J. Lond. Math. Soc. 10(3), 295–305 (1975)
  • Kokilashvili, V., Meskhi, A., Zaighum, M.A.: Weighted kernel operators in variable exponent amalgam spaces. J. Inequal. Appl. (2013). ...
  • Kolmogorov, A.N.: Über Kompaktheit der Funktionenmengen bei der Konvergenz im Mittel. Nachr. Ges. Wiss. Göttingen 9, 60–63 (1931)
  • Kováčik, O., Rákosník, J.: On spaces $$ L^{p(x)}$$ and $$W^{k, p(x)}$$. Czechoslovak Math. J. 41(116)(4), 592–618 (1991)
  • Kulak, O., Gurkanli, A.T.: Bilinear multipliers of weighted Wiener amalgam spaces and variable exponent Wiener amalgam spaces. J. Inequal....
  • Lahmi, B., Azroul, E., El Haitin, K.: Nonlinear degenerated elliptic problems with dual data and nonstandard growth. Math. Rep. 20(70)(1),...
  • Liu, Q.: Compact trace in weighted variable exponent Sobolev spaces $$W^{1, p(x)}\left( \varOmega ,\upsilon _{0},\upsilon _{1}\right) $$....
  • Meskhi, A., Zaighum, M.A.: On the boundedness of maximal and potential operators in amalgam spaces. J. Math. Inequal. 8(1), 123–152 (2014)
  • Musielak, J.: Orlicz Spaces and Modular Spaces. Lecture Notes in Mathematics, 1034. Springer, Berlin (1983)
  • Pandey, S.S.: Compactness in Wiener amalgams on locally compact groups. Int. J. Math. Math. Sci. 2003(55), 3503–3517 (2003)
  • Rafeiro, H.: Kolmogorov compactness criterion in variable exponent Lebesgue spaces. Proc. A. Razmadze Math. Inst. 150, 105–113 (2009)
  • Squire, M.L.T.: Amalgams of $$L^{p}$$ and $$l^{q}$$. Ph.D. Thesis, McMaster University (1984)
  • Sudakov, V.N.: Criteria of compactness in function spaces. Upsekhi Math. Nauk. 12, 221–224 (1957). (in Russian)
  • Takahashi, T.: On the compactness of the function-set by the convergence in the mean of general type. Studia Math. 5, 141–150 (1934)
  • Weil, A.: L’integration Dans Les Groupes Topologiques et Ses Applications. Hermann et Cie, Paris (1940)
  • Wiener, N.: On the representation of functions by trigonometrical integrals. Math. Z. 24, 575–616 (1926)
  • Yosida, K.: Functional Analysis. Springer, Berlin (1980)