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Trudinger’s exponential integrability for Riesz potentials of functions in generalized grand Morrey spaces. (English) Zbl 1305.42017

Summary: Our aim in this paper is to discuss Trudinger’s exponential integrability for Riesz potentials of functions in generalized grand Morrey spaces. Our result will imply the boundedness of the Riesz potential operator from a grand Morrey space to a Morrey space.

MSC:

42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
42B25 Maximal functions, Littlewood-Paley theory
42B35 Function spaces arising in harmonic analysis
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
47G40 Potential operators
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[1] Fusco, N.; Lions, P. L.; Sbordone, C., Sobolev embedding theorems in borderline cases, Proc. Amer. Math. Soc., 124, 561-565 (1996) · Zbl 0841.46023
[2] Iwaniec, T.; Sbordone, C., On the integrability of the Jacobian under minimal hypotheses, Arch. Ration. Mech. Anal., 119, 129-143 (1992) · Zbl 0766.46016
[3] Iwaniec, T.; Sbordone, C., Weak minima of variational integrals, J. Reine Angew. Math., 454, 143-161 (1994) · Zbl 0802.35016
[4] Iwaniec, T.; Sbordone, C., Riesz transforms and elliptic PDEs with VMO coefficients, J. Anal. Math., 74, 183-212 (1998) · Zbl 0909.35039
[5] Meskhi, A., Maximal functions, potentials and singular integrals in grand Morrey spaces, Complex Var. Elliptic Equ., 56, 10-11, 1003-1019 (2011) · Zbl 1261.42022
[6] Mizuta, Y., Potential Theory in Euclidean Spaces (1996), Gakkōtosho: Gakkōtosho Tokyo
[7] 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, 425-436 (2008) · Zbl 1175.31005
[8] Morrey, C. B., On the solutions of quasi-linear elliptic partial differential equations, Trans. Amer. Math. Soc., 43, 126-166 (1938) · JFM 64.0460.02
[9] Nakai, E., Hardy-Littlewood maximal operator, singular integral operators and the Riesz potentials on generalized Morrey spaces, Math. Nachr., 166, 95-103 (1994) · Zbl 0837.42008
[10] Peetre, J., On the theory of \(L_{p, \lambda}\) spaces, J. Funct. Anal., 4, 71-87 (1969) · Zbl 0175.42602
[11] Sbordone, C., Grand Sobolev spaces and their applications to variational problems, Matematiche (Catania), 51, 335-347 (1997) · Zbl 0915.46030
[12] Sbordone, C., Nonlinear elliptic equations with right hand side in nonstandard spaces, Atti Semin. Mat. Fis. Univ. Modena, 46, Suppl., 361-368 (1998), Dedicated to Prof. C. Vinti, Perugia, 1996 (in Italian) · Zbl 0913.35050
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