Modular estimates for nonlinear integral operators and applications in fractional calculus

Numerical Functional Analysis and Optimization

Volumn 17, Issue 1-2, 1996, Pages 143-165

  Mantellini, Ilaria ^a   Vinti, Gianluca ^a  

^a UNIVERSITY OF PERUGIA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0347699499     PISSN: 01630563     EISSN: None     Source Type: Journal    
DOI: 10.1080/01630569608816688     Document Type: Article

References (32)

1. F. BARBIERI.: Approssimazione mediante nuclei momento. Atti Sem. Mat. Fis. Univ. Modena, 32 (1983), 308-328.
2. C. BARDARO - G. VINTI.: Modular estimates of integral operators with homogeneous kernels in Orlicz type classes. Results in Mathematics 19 (1991), 46-53.
3. C. BARDARO - G. VINTI.: Some estimates of certain integral operators in generalized fractional Orlicz classes. Numer. Funct. Anal. and Optimiz. 12 (1991), 443-453.
4. C. BARDARO - G. VINTI.: Some inclusion theorems for Orlicz and Musielak-Orlicz type spaces. in print in Ann. Mat. Pura e Appl.
5. C. BARDARO - J. MUSIELAK - G. VINTI.: Modular estimates and modular convergence for a class of nonlinear operators. Mathematica Japonica 39, No. 1 (1994), 7-14.
6. C. BARDARO - G. VINTI.. Modular estimates for linear integral operators in Musielak-Orlicz spaces on groups to appear in Atti Sem. Mat. Fis. Univ. Modena.
7. C. BARDARO - G. VINTI.: Modular approximation by nonlinear integral operators on locally compact groups. submitted to Commentationes Mathematicae.
8. P.L. BUTZER - F. FEHÉR.: Generalized Hardy and Hardy Littlewood inequalities in rearrangement-invariant spaces. Comment. Math. Prace Univ. Tomus specialis in Honorem L. Orlicz I (1978), 41-64.
9. P.L. BUTZER - R.J. NESSEL.: Fourier Analysis and Approximation. Academic Press, New York / London, 1971.
10. A. ERDÉLYL: On fractional integration and its application to the Theory of Hankel trasforms. Quart. J. Math. 11 (1940), 293.
11. F. FEHÉR.: A note on a paper of E.R. Love. Bull. Austral. Math. Soc. 19 (1978), 67-75.
12. F. FEHÉR.: A generalized Schur-Hardy inequality on normed Köthe spaces. General Inequalities II (Proc. 2nd. Int. Conf. on General Inequalities, Oberwolfach, 1978), Birkhäuser, Basel, 1980, 277-285.
13. G.B. FOLLAND.: Real Analysis: Modern techniques and their applications. Wiley and Sons, 1984.
14. A. GOGATISHVILI - V. KOKILASHVILI.: Criteria of weighted inequalities in Orlicz classes for maximal functions defined on homogeneous type spaces. Proceedings of the Georgian Academy of Sciences. Mathematics 1, (1993), No. 6, 617-649.
15. E. HEWITT - K.A. ROSS.: Abstract Harmonic Analysis. Springer-Verlag, Berlin - Göttingen, 1963.
16. Φ(Ω). Commentationes Math. 22 (1981), 245-255.
17. H. KOBER.: On fractional integrals and derivatives. Quart. J. Math. 11 (1940), 193.
18. W.M. KOZLOWSKI.: Modular Function Spaces (Pure Appl. Math.). Marcel Dekker, New York and Basel, 1988.
19. E.R. LOVE.: Some inequalities for fractional integrals. Linear spaces and approximation (Proc. Conf. Mathematical Research Institute, Oberwolfach, 1977, 177-181. International Series of Numerical Mathematics, 10. Birkhäuser Verlag, Basel Stuttgart, 1978).
20. C. MARTINEZ - M. SANZ - D. MARTINEZ.: About fractional integrals in the space of locally integrable functions. J. Math. Anal. Appl., 167 (1992), 111-122.
21. J. MIKUSINSKI.: Operational Calculus. Pergamon Press, Warszawa, 1959.
22. H. MUSIELAK - J. MUSIELAK.: An application of a Bernstein-type inequality for fractional derivatives to some problems of modular spaces. Constructive Function Theory 1977, Sofia (1980), 427-432.
23. H. MUSIELAK.: On the τ-modulus of smoothness in generalized Orlicz spaces. Commentationes Math., Prace Mat. XXV (1985), 285-293.
24. J. MUSIELAK.: Orlicz spaces and modular spaces. Lect. Notes Math. 1034, 1983.
25. J. MUSIELAK.: On sequentially M-integrable distributions. Studia Mathematica, T. LXXVII. (1984).
26. J. MUSIELAK.: Approximation by Nonlinear Singular Integral Operators in Generalised Orlicz Spaces. Commentationes Mathematicae, XXXI (1991), 79-88.
27. J. MUSIELAK.: Nonlinear Approximation in some modular function spaces.I. Mathematica Japonica, Vol. 38, No. 1, (1993), 83-90.
28. J. MUSIELAK.: On the approximation by nonlinear integral operators with generalized Lipschitz kernel over a compact abelian group. Commentationes Mathematicae, XXXIII (1993), 99-104.
29. J. MUSIELAK.: On the approximation by nonlinear integral operators with generalized Lipschitz kernel over a locally compact abelian group. to appear in Commentationes Mathematicae.
30. K.B. OLDHAM - J. SPANIER.: The fractional calculus. Academic Press, New York, 1974.
31. M.M. RAO - Z.D. REN.: Theory of Orlicz spaces. Pure and Applied Mathematics, Marcel Dekker, Inc. New York, Basel, Hong Kong, 1991.
32. V. ZANELLI.: Funzioni momento convergenti dal basso in variazione di ordine non intero. Atti Sem. Mat. Fis. Univ. Modena, 30 (1981), 355-369.