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Complex Variables and Elliptic Equations
An International Journal
Volume 56, 2011 - Issue 10-11: A tribute to Victor I. Burenkov; Guest Editors: Robert P. Gilbert, Massimo Lanza de Cristoforis and Alexander Pankov
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Original Articles

Boundedness of integral operators from weighted Sobolev space to weighted Lebesgue space

R. Oinarov L.N. Gumilyov Eurasian National University, 5 Munaytpasov St, Astana 010008, KazakhstanCorrespondence[email protected]
Pages 1021-1038 | Received 17 Sep 2010, Accepted 11 Feb 2011, Published online: 12 Jul 2011

References

  • Oinarov , R . 1993 . On weighted norm inequalities with three weights . J. London Math. Soc. , 2 ( 48 ) : 103 – 116 .
  • Oinarov , R and Otelbayev , M . 1988 . Criteria for the discreteness of the spectrum of a general Sturm–Liouville operator and related imbedding theorems . Differentsial'nye Uravneniya , 4 ( 24 ) : 584 – 591 .
  • Stepanov , VD and Ushakova , EP . 2001 . On integral operators with variable limits of integration . Proc. Steklov Inst. Math. , 232 : 290 – 309 .
  • Oinarov , R . 1991 . Weighted inequalities for one class of integral operators . Dokl. Akad. Nauk SSSR , 5 ( 319 ) : 1076 – 1078 .
  • Oinarov , R . 2003 . Reversion of Holder type inequalities for sums of weighted norms and additive weighted estimates of integral operators . Math. Ineq. Appl. , 3 ( 6 ) : 221 – 236 .
  • Oinarov , R . 2002 . Weighted estimate of intermediate operator on cone of non-negative functions . Siberian Math. J. , 1 ( 43 ) : 161 – 173 .
  • Heinig , HP and Lai , Q . 2000 . Weighted modular inequalities for Hardy-type operators on monotone functions . J. Ineq. Pure Appl. Math. , 1 ( 1 ) : 1 – 25 .
  • Stepanov , VD and Ushakova , EP . 2010 . Kernel operators with variable intervals of integration in Lebesgue spaces and applications . Math. Ineq. Appl. , 3 ( 13 ) : 449 – 510 .
  • Edmunds , DE and Stepanov , VD . 1995 . On the singular numbers of certain Volterra integral operators . J. Func. Anal. , 1 ( 134 ) : 222 – 246 .
  • Stepanov , VD . 2000 . On the lower bounds for Schatten–von–Neumann norms of certain Volterra integral operators . J. London Math. Soc. , 2 ( 61 ) : 905 – 922 .
  • Chen , T and Sinnamon , G . 2002 . Generalized Hardy operators and normalizing measures . J. Ineq. Appl. , 7 : 829 – 866 .
  • Oinarov , R . 1994 . Two-sided norm estimates for certain classes of integral operators . Proc. Steklov Inst. Math. , 204 : 205 – 214 .
  • Heinig , HP and Sinnamon , G . 1998 . Mapping properties of integral averaging operators . Studia Math. , 129 : 157 – 177 .
  • Gogatishvili , A and Lang , J . 1999 . The generalized Hardy operators with kernel and variable limits in Banach function spaces . J. Ineq. Appl. , 4 : 1 – 16 .
  • Oinarov , R . 2007 . Boundedness and compactness of integral operators of Volterra type . Siberian Math. J. , 5 ( 48 ) : 1100 – 1115 .
  • Batuyev , EN and Stepanov , VD . 1987 . Weighted inequalities of Hardy type , 22; Vladivostok : Preprint VC DVNC AN SSSR . Ref. J. Mat. 1987, 6B69
  • Batuyev , EN and Stepanov , VD . 1989 . On weighted inequalities of Hardy type . Siberian Math. J. , 30 : 8 – 16 .

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