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Original Articles

Maximal functions, potentials and singular integrals in grand Morrey spaces

Pages 1003-1019 | Received 18 Jul 2010, Accepted 13 Oct 2010, Published online: 16 Mar 2011

References

  • Iwaniec , T and Sbordone , C . 1992 . On the integrability of the Jacobian under minimal hypotheses . Arch. Rational Mech. Anal. , 119 : 129 – 143 .
  • Greco , L , Iwaniec , T and Sbordone , C . 1997 . Inverting the p-harmonic operator . Manuscripta Math. , 92 : 249 – 258 .
  • Fiorenza , A . 2000 . Duality and reflexivity in grand Lebesgue spaces . Collect. Math. , 51 ( 2 ) : 131 – 148 .
  • Fiorenza , A and Karadzhov , GE . “ Grand and small Lebesgue spaces and their analogs ” . In Consiglio Nazionale delle Ricerche , Istituto per le Applicazioni del Calcolo ‘Mauro Picone’ . Raporto Technico No. 316/06
  • Capone , C and Fiorenza , A . 2005 . On small Lebesgue spaces . J. Funct. Spaces Appl. , 3 : 73 – 89 .
  • Fiorenza , A , Gupta , B and Jain , P . 2008 . The maximal theorem in weighted grand Lebesgue spaces . Stud. Math. , 188 ( 2 ) : 123 – 133 .
  • Kokilashvili , V and Meskhi , A . 2009 . A note on the boundedness of the Hilbert transform in weighted grand Lebesgue spaces . Georgian Math. J. , 16 ( 3 ) : 547 – 551 .
  • Kokilashvili , V . 2009 . Boundedness criterion for the Cauchy singular integral operator in weighted grand Lebesgue spaces and application to the Riemann problem . Proc. A. Razmadze Math. Inst. , 151 : 129 – 133 .
  • Meskhi , A . Criteria for the boundedness of potential operators in grand Lebesgue spaces, 2010 , Available at http://arxiv.org/PS_cache/arxiv/pdf/1007/1007.1185v1.pdf
  • Morrey , CB . 1938 . On the solutions of quasi-linear elliptic partial differential equations . Trans. Am. Math. Soc. , 43 : 126 – 166 .
  • Adams , DR . 1975 . A note on Riesz potentials . Duke Math. J. , 42 ( 4 ) : 765 – 778 .
  • Peetre , J . 1969 . On the theory of ℒ p,λ spaces . J. Funct. Anal. , 4 : 71 – 87 .
  • Chiarenza , F and Frasca , M . 1987 . Morrey spaces and Hardy–Littlewood maximal function . Rend. Math. , 7 : 273 – 279 .
  • Di Fazio , G and Ragusa , MA . 1991 . Commutators and Morrey spaces . Boll. U.M.I. , 7 ( 5-A ) : 323 – 332 .
  • Sawano , Y and Tanaka , H . 2005 . Morrey spaces for nondoubling measures . Acta Math. Sin. , 21 ( 6 ) : 1535 – 1544 .
  • Giaquinta , M . 1983 . Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems , Princeton, NJ : Princeton University Press .
  • Burenkov , V and Guliyev , HV . 2004 . Necessary and sufficient conditions for boundedness of the maximal operator in local Morrey-type spaces . Stud. Math. , 163 ( 2 ) : 157 – 176 .
  • Burenkov , VI , Guliev , VS and Guliev , GV . 2007 . Necessary and sufficient conditions for the boundedness of the Riesz potential in local Morrey-type spaces (Russian) . Dokl. Akad. Nauk. , 412 ( 5 ) : 585 – 589 . English Trans.: Dokl. Math. 75(1) (2007), pp. 103–107
  • Strömberg , JO and Torchinsky , A . 1989 . “ Weighted Hardy Spaces ” . In Lecture Notes in Mathematics , Vol. 1381 , Berlin : Springer Verlag .
  • Coifman , RR and Weiss , G . 1971 . “ Analyse Harmonique Non-commutative sur Certains Espaces Homogénes ” . In Lecture Notes in Mathematics , Vol. 242 , Berlin : Springer-Verlag .
  • Duandikoetxea , J . 2001 . “ Fourier Analysis ” . In Graduate Studies in Mathematics , Vol. 29 , Providence, RI : AMS .
  • Kokilashvili , V and Meskhi , A . 2008 . Maximal and singular integrals in Morrey spaces with variable exponent . Arm. J. Math. , 1 : 18 – 28 .
  • Edmunds , DE , Kokilashvili , V and Meskhi , A . 2002 . “ Bounded and Compact Integral Operators ” . In Mathematics and its Applications , Dordrecht, Boston, London : Kluwer Academic Publishers .
  • Hedberg , L . 1972 . On certain convolution inequalities . Proc. Am. Math. Soc. , 36 : 505 – 510 .
  • Eridani , A , Kokilashvili , V and Meskhi , A . 2009 . Morrey spaces and fractional integral operators . Expo. Math. , 27 : 227 – 239 .
  • Kokilashvili , V and Meskhi , A . 2010 . Maximal functions and potentials in variable exponent Morrey spaces with non-doubling measure . Complex Var. Elliptic Eqns. , 55 ( 8 ) : 923 – 936 .

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