Hardy inequalities in fractional Orlicz-Sobolev spaces

• Autores: ARIEL M. SALORT
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 66, Nº 1, 2022, págs. 183-195
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • In this article we prove both norm and modular Hardy inequalities for class functions in one-dimensional fractional Orlicz–Sobolev spaces.

• Referencias bibliográficas
  • R. Adams, N. Aronszajn, and K. T. Smith, Theory of Bessel potentials. II, Ann. Inst. Fourier (Grenoble) 17(2) (1967), 1–135. DOI: 10.5802/aif.265.
  • A. Alberico, A. Cianchi, L. Pick, and L. Slav´ıkova´, Fractional Orlicz– Sobolev embeddings, J. Math. Pures Appl. (9) 149 (2021), 216–253....
  • N. Aronszajn and K. T. Smith, Theory of Bessel potentials. I, Ann. Inst. Fourier (Grenoble) 11 (1961), 385–475. DOI: 10.5802/aif.116.
  • S. Bloom and R. Kerman, Weighted norm inequalities for operators of Hardy type, Proc. Amer. Math. Soc. 113(1) (1991), 135–141. DOI: 10.2307/2048449.
  • S. Bloom and R. Kerman, Weighted LΦ integral inequalities for operators of Hardy type, Studia Math. 110(1) (1994), 35–52. DOI: 10.4064/sm-110-1-35-52.
  • S. Bloom and R. Kerman, Weighted Orlicz space integral inequalities for the Hardy–Littlewood maximal operator, Studia Math. 110(2) (1994),...
  • J. S. Bradley, Hardy inequalities with mixed norms, Canad. Math. Bull. 21(4) (1978), 405–408. DOI: 10.4153/CMB-1978-071-7.
  • A. Cianchi, Hardy inequalities in Orlicz spaces, Trans. Amer. Math. Soc. 351(6) (1999), 2459–2478. DOI: 10.1090/S0002-9947-99-01985-6.
  • P. De Napoli, J. Fernández Bonder, and A. Salort, A Pólya–Szegö principle for general fractional Orlicz–Sobolev spaces, Complex Var. Elliptic...
  • E. Di Nezza, G. Palatucci, and E. Valdinoci, Hitchhiker’s guide to the fractional Sobolev spaces, Bull. Sci. Math. 136(5) (2012), 521–573....
  • J. Fernandez Bonder, M. Pérez-Llanos, and A. M. Salort , A H¨older infinity Laplacian obtained as limit of Orlicz fractional Laplacians, Rev....
  • J. Fernandez Bonder and A. M. Salort, Fractional order Orlicz–Sobolev spaces, J. Funct. Anal. 277(2) (2019), 333–367. DOI: 10.1016/j.jfa.2019.04....
  • R. L. Frank and R. Seiringer, Non-linear ground state representations and sharp Hardy inequalities, J. Funct. Anal. 255(12) (2008), 3407–3430....
  • P. Grisvard, Espaces intermédiaires entre espaces de Sobolev avec poids, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 17(3) (1963), 255–296.
  • G. H. Hardy, Note on a theorem of Hilbert, Math. Z. 6(3–4) (1920), 314–317. DOI: 10.1007/BF01199965.
  • H. P. Heinig and L. Maligranda, Interpolation with weights in Orlicz spaces, Boll. Un. Mat. Ital. B (7) 8(1) (1994), 37–55.
  • I. W. Herbst, Spectral theory of the operator (p2 + m2)1/2 − Ze2/r, Comm. Math. Phys. 53(3) (1977), 285–294. DOI: 10.1007/BF01609852..
  • G. N. Jakovlev, Boundary properties of a class of functions, Trudy Mat. Inst. Steklov 60 (1961), 325–349.
  • M. A. Krasnosel’ski˘ı and Ja. B. Ruticki˘ı, “Convex Functions and Orlicz Spaces”, Translated from the first Russian edition by Leo F. Boron,...
  • N. Krugljak, L. Maligranda, and L. E. Persson, On an elementary approach to the fractional Hardy inequality, Proc. Amer. Math. Soc. 128(3)...
  • A. Kufner, O. John, and S. Fucik, “Function Spaces”, Vol. 3, Springer Netherlands, 1979.
  • A. Kufner, L.-E. Persson, and N. Samko, “Weighted Inequalities of Hardy Type”, Second edition, World Scientific Publishing Co. Pte. Ltd.,...
  • Q. Lai, Two weight mixed Φ-inequalities for the Hardy operator and the Hardy– Littlewood maximal operator, J. London Math. Soc. (2) 46(2)...
  • A. Maione, A. M. Salort, and E. Vecchi, Maz’ya–Shaposhnikova formula in magnetic fractional Orlicz–Sobolev spaces Asymptot. Anal. (2021),...
  • L. Maligranda, Generalized Hardy inequalities in rearrangement invariant spaces, J. Math. Pures Appl. (9) 59(4) (1980), 405–415.
  • B. Opic and A. Kufner, “Hardy-type Inequalities”, Pitman Research Notes in Mathematics Series 219, Longman Scientific & Technical, Harlow,...
  • P. Palmieri, Un approccio alla teoria degli spazi di traccia relativi agli spazi di Orlicz–Sobolev, Boll. Un. Mat. Ital. B (5) 16 (1979),...
  • M. M. Rao and Z. D. Ren, “Applications of Orlicz Spaces”, Monographs and Textbooks in Pure and Applied Mathematics 250, Marcel Dekker, Inc.,...
  • A. M. Salort, Eigenvalues and minimizers for a non-standard growth non-local operator, J. Differential Equations 268(9) (2020), 5413–5439....
  • G. Talenti, Osservazioni sopra una classe di disuguaglianze, Rend. Sem. Mat. Fis. Milano 39 (1969), 171–185. DOI: 10.1007/BF02924135.
  • G. Tomaselli, A class of inequalities, Boll. Un. Mat. Ital. (4) 2 (1969), 622–631.