Continuity of superposition operators on w 0 and W 0

Ryszard Płuciennik

Commentationes Mathematicae Universitatis Carolinae (1990)

  • Volume: 031, Issue: 3, page 529-542
  • ISSN: 0010-2628

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Płuciennik, Ryszard. "Continuity of superposition operators on $w_0$ and $W_0$." Commentationes Mathematicae Universitatis Carolinae 031.3 (1990): 529-542. <http://eudml.org/doc/17875>.

@article{Płuciennik1990,
author = {Płuciennik, Ryszard},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Lebesgue sequence space; Lebesgue function space; continuity of the superposition operator; space of all sequences or all functions Cesáro strongly summable},
language = {eng},
number = {3},
pages = {529-542},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Continuity of superposition operators on $w_0$ and $W_0$},
url = {http://eudml.org/doc/17875},
volume = {031},
year = {1990},
}

TY - JOUR
AU - Płuciennik, Ryszard
TI - Continuity of superposition operators on $w_0$ and $W_0$
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1990
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 031
IS - 3
SP - 529
EP - 542
LA - eng
KW - Lebesgue sequence space; Lebesgue function space; continuity of the superposition operator; space of all sequences or all functions Cesáro strongly summable
UR - http://eudml.org/doc/17875
ER -

References

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  1. Appell J., Upper estimates for superposition operators and some applications, Ser. A I, Ann. Acad. Sci. Fenn. 8 (1983), 149-159. (1983) Zbl0489.47017MR0698843
  2. Appell J., Zabrejko P. P., Sharp upper estimates for the superposition operator, Doklady Akad. Nauk BSSR 27 (1983), 686-689. (1983) Zbl0525.47020MR0714619
  3. Chew Tuan Seng, Characterization of orthogonally additive operators on sequence spaces, SEA Bull. Math. 11 (1987), 39-44. (1987) Zbl0635.46008MR0914362
  4. Chew Tuan Seng, Superposition operators on w 0 and W 0 , to appear, Comment. Math. 
  5. Chew Tuan Seng, Lee Peng Yee, Orthogonally additive functionals on sequence spaces, SEA Bull. Math. 9 (1985), 81-85. (1985) Zbl0613.46007MR0850699
  6. Dedagich F., Zabrejko P. P., On the superposition operator in l p spaces, (Russian), Sibirskij Mat. Zhurn. 28 (1987), 86-98. (1987) Zbl0632.47046MR0886856
  7. Krasnoselki M. A., On the continuity of the operator F u ( x ) = f ( x , u ( x ) ) , , (Russian), Doklady Akad. Nauk SSSR 77 (1951), 185-188. (1951) MR0041354
  8. Krasnoselki M. A., Zabrejko P. P., Pustylnik Ye. L, Sobolevskii P. Ye., Integral operators in spaces of summable functions, Nauka, (Russian), Moskva 1966. (1966) MR0206751
  9. Lee Peng Yee, Sectionally modulared spaces and strong summability, Tomus specialis in honorem Orlicz, Comment. Math. 1 (1978), 197-203. (1978) Zbl0404.46004MR0504164
  10. Maddox I. J., Elements of functional analysis, Cambridge University Press 1970. (1970) Zbl0193.08601MR0390692
  11. Pluciennik R., Boundedness of superposition operator on w 0 , to appear, SEA Bull. Math. 15 (1991). (1991) Zbl0748.47022MR1145435
  12. Pluciennik R., Boundedness of the superposition operator in generalized Orlicz spaces of vector-valued functions, Bull. Pol. Ac.: Math. 33 (1985), 531-540. (1985) Zbl0587.46027MR0826380
  13. Pluciennik R., On some properties of the superposition operator in generalized Orlicz spaces of vector-valued functions, Comment. Math. 25 (1985), 321-337. (1985) Zbl0608.47068MR0844649
  14. Robert J., Continuité d'un opérateur nonlinéar sur certains espaces de suites, Paris, Ser. A., C.R. Acad. Sci. 259 (1964), 1287-1290. (1964) Zbl0196.44602MR0166602
  15. Shragin I. V., Conditions for imbedding of classes and their consequences, (Russian), Mat. Zametki 20 (1976), 681-692. (1976) MR0442641

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