Some estimates of certain integral operators in generalized fractional orlicz classes

References

• Barbieri , F. 1983 . Approssimazione mediante nuclei momento . Atti Sem. Mat. Fis. Univ. Modena , 32 : 308 – 328 .
   Google Scholar
• Bardaro , C. 1984 . On approximation properties for some classes of linear operators of convolution type . Atti Sem. Mat. Fis. Univ. Modena , 33 : 329 – 356 .
   Google Scholar
• Bardaro , C. and Vinti , G. 1990 . On approximation properties of certain nonconvolution integral operators . Journal of Approximation Theory , 62 ( 3 ) : 358 – 371 .
   Web of Science ®Google Scholar
• Bardaro , C. and Vinti , G. 1988 . “ Integral operators on vector measures and applications to the moment kernel $title:Rendiconti di Matematica ” . In Rendiconti di Matematica Vol. 8 , 149 – 164 . Roma
   Google Scholar
• Bardaro , C. and Vinti , G. 1989 . Modular convergence in generalized Orlicz spaces for oment type operators $title:Applicable Analysis . Applicable Analysis , 32 : 265 – 276 .
   Google Scholar
• Bardaro , C. and Vinti , G. 1991 . On convergence of moment operators with respect to ϕ-variation . Applicable Analysis , 41 : 247 – 256 .
   Google Scholar
• Bardaro , C. and Vinti , G. 1991 . Modular estimates of integral operators with homogeneous kernel in Orlicz type spaces . Results in Mathematics , 19 : 46 – 53 .
   Google Scholar
• Bardaro , C. and Vinti , G. Some estimates of integral operators with respect to the multidimensional Vitali ϕ-variation, and applications in fractional calculus , Roma : Rendiconti di Matematica . To appear in
   Google Scholar
• Butzer , P. L. and Fehér , F. 1978 . “ Generalized Hardy and Hardy-Littlewood inequalities in rearrangement-invariant spaces ” . Vol. 1 , 41 – 64 . Comment. Math. Prace Univ. Tomus specialis in Honorem L. Orlicz .
   Google Scholar
• Butzer , P. L. and Westphal , U. An access to fractional differentiation via fractional difference quotiens. In Fractional Calculus and its Applications . Proceedings of the Int. Conf. Univ. New-Haden. pp. 116 – 145 . Springer-Verlag .
   Google Scholar
• Cattelani , F. 1981 . Nuclei di tipo distanza che attutiscono i salti in una o piú variabili . Atti Sem. Mat. Fis. Univ. Modena , 30 : 299 – 321 .
   Google Scholar
• Erdélyi , A. 1940 . On fractional integration and its application to the Theory of Hankel transforms Quart . J. Math. , 11 : 293
   Google Scholar
• Fehér , F. 1978 . A note on a paper of E.R. Love . Bull. Austral. Math. Soc , 19 : 67 – 75 .
   Google Scholar
• Fehér , F. A generalized Schur-Hardy inequality on normed Kothe spaces. General Inequalities II . Proc. Int. Conf. on General Inequalities Oberwolfach . 2nd 1978 . pp. 277 – 285 . Basel : Birkhauser .
   Google Scholar
• Kober , H. 1940 . On fractional integrals and derivatives . Quart. J. Math , 11 : 193
   Google Scholar
• Kozlowski , W. M. 1988 . Modular Function Spaces , New York and Basel : Pure Appl. Math. Marcel Dekker .
   Google Scholar
• Love , E. R. Some inequalities for fractional integrals. Linear spaces and approximation, International Series of Numerical Mathematics . Proc. Conf. Mathematical Research Institute Oberwolfach . 1977 . Vol. 40 , pp. 177 – 184 . Basel, Stuttgart : Birkhauser Verlag .
   Google Scholar
• Mikusinski , J. 1959 . Operational Calculus , Warszava : Pergamon Press .
   Google Scholar
• Musielak , J. 1983 . Orlicz spaces and modular spaces , Vol. 1034 , Springer-Verlag . Lecture Notes in Math
   Google Scholar
• Oldham , K. B. and Spainer , J. 1974 . The Fractional Calculus , New York : Academic Press .
   Google Scholar
• Zanelli , V. 1981 . I polinomi di Stieltjes approssimanti in variazione di ordine non intero . Atti Sem. Mat. Fis. Univ. Modena , 30 : 151 – 175 .
   Google Scholar
• Zanelli , V. 1981 . Funzioni momento convergent dal basso in variazione di ordine non intero . Atti Sem. Mat. Fis. Univ. Modena , 30 : 355 – 369 .
   Google Scholar