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Myrzagaliyeva, Aigul (2016) On pointwise multipliers in some function spaces. [Ph.D. thesis]

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Abstract (english)

By a pointwise multiplier from a function space X into another function space Y, we mean a function which defines a bounded linear mapping of X into Y by pointwise multiplication. Pointwise multipliers arise in many different areas of mathematical analysis and its applications. For example, the coefficients of differential operators are often assumed to be pointwise multipliers of function spaces. The solutions of boundary value problems can be sought in the class of multipliers. The thesis consists of 3 Chapters and is organized as follows. Chapter 1 contains necessary and sufficient conditions for the boundedness of one variable differential operators acting from a weighted Sobolev space to a weighted Lebesgue space on the positive real half line. Chapter 2 is concerned with the characterization of spaces of multipliers for a pair of weighted Sobolev spaces. In Chapter 3, we give the description of the space of multipliers (1<p<n/l). In addition, here we solve the boundedness problem of the Schrodinger operator.

Abstract (italian)

Per moltiplicatore puntuale di uno spazio funzionale X in un altro spazio funzionale Y intendiamo una funzione che definisce un operatore di moltiplicazione puntuale lineare e limitato di X in Y. I moltiplicatori puntuali si presentano in molte aree differenti dell'analisi matematica e delle sue applicazioni. I coefficienti di operatori differenziali e pi`u in generale di simboli di operatori pseudodifferenziali sono spesso presi come moltiplicatori puntuali di spazi funzionali. Le soluzioni di problemi al contorno possono essere ricercate in classi di moltiplicatori. La tesi consiste di 3 capitoli ed \`e strutturata nel modo seguente. Nel Capitolo 1 contiene anche condizioni necessarie e sufficienti per la limitatezza di operatori differenziali in una variabile che agiscono da uno spazio di Sobolev con peso in uno spazio di Lebesgue con peso sulla semiretta reale positiva. Il Capitolo 2 concerne la caratterizzazione dello spazio dei moltiplicatori. Nel Capitolo 3 diamo la descrizione dello spazio (1<p<n/l). Inoltre risloviamo qui il problema della limitatezza dell'operatore di Schrodinger .

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EPrint type:Ph.D. thesis
Tutor:Kussainova, L. and Lanza de Cristoforis, Massimo
Ph.D. course:Ciclo 28 > Scuole 28 > SCIENZE MATEMATICHE > MATEMATICA
Data di deposito della tesi:29 April 2016
Anno di Pubblicazione:29 April 2016
Key Words:Pointwise multiplier, Sobolev space, weighted Sobolev space, differential operator
Settori scientifico-disciplinari MIUR:Area 01 - Scienze matematiche e informatiche > MAT/05 Analisi matematica
Struttura di riferimento:Dipartimenti > Dipartimento di Matematica
Centri > Centro di Matematica applicata
Codice ID:9638
Depositato il:05 Dec 2018 14:04
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Bibliografia

I riferimenti della bibliografia possono essere cercati con Cerca la citazione di AIRE, copiando il titolo dell'articolo (o del libro) e la rivista (se presente) nei campi appositi di "Cerca la Citazione di AIRE".
Le url contenute in alcuni riferimenti sono raggiungibili cliccando sul link alla fine della citazione (Vai!) e tramite Google (Ricerca con Google). Il risultato dipende dalla formattazione della citazione.

1) V.G. Maz'ya, T.O. Shaposhnikova, Cerca con Google

"Theory of multipliers in spaces of differentiable functions". Cerca con Google

Pitman, Boston, 1985. Cerca con Google

2) V.G. Maz'ya, T.O. Shaposhnikova, "Theory of Sobolev multipliers. Cerca con Google

With applications to differential and integral operators". Cerca con Google

Grundlehren der Mathematischen Wissenschaften, Springer-Verlag, Berlin, 2009. Cerca con Google

3) G. Nariman, Smooth pointwise multipliers of modulation spaces. An. Stiint. Univ. "Ovidius" Constanta Ser. Mat. 20/1 (2012), 317--327. Cerca con Google

4) F. Beatrous, J. Burbea, On multipliers for Hardy-Sobolev spaces. Proc. Amer. Math. Soc. 136/6 2008, 2125--2133. Cerca con Google

5) M.-R. Pierre Gilles, Multipliers and Morrey spaces. Potential Anal. 38/3 (2013), 741--752. Cerca con Google

6) S. Bloom, Pointwise multipliers of weighted BMO spaces. Cerca con Google

Proc. Amer. Math. Soc. 105/4 (1989), 950--960. Cerca con Google

7) Y. Han, F. Liao, Z. Liu, Pointwise multipliers on spaces of homogeneous type in the sense of Coifman and Weiss. Hindawi Publishing Corporation Abstract and Applied Anal. Volume 2014 (2014), Article ID 164624. Cerca con Google

8 Y. Han, Pointwise multipliers of Besov spaces on Carnot-Caratheodory spaces. Journal of Mathematical Analysis and Appl. 396/2 (2012), 578--589. Cerca con Google

9) M. Meyries, M. Veraar, Pointwise multiplication on vector-valued function spaces with power weights. Journal of Fourier Analysis and Appl. 21/1 (2015), 95--136. Cerca con Google

10) M. Otelbaev, K.T. Mynbayev "Weighted function spaces and a range of differential operations". Nauka, Moscow, 1988. Cerca con Google

11) M. Otelbaev, Two sided estimates of the distribution of Cerca con Google

the eigenvalues of the Sturm-Liouville operator. Math. Notes. 20/6 (1976), 859--867. Cerca con Google

12) M. Otelbaev, "Spectrum estimates of the Sturm-Liouville operator". Gyilyim, Alma-ata, 1990. Cerca con Google

13) M. Otelbaev, Embedding theorems for spaces with a weight and their application to the study of the spectrum of the Schrodinger operator. Trudy Matematicheskogo Instituta im. V.A. Steklova. 150 (1979), 265--305. Cerca con Google

14) M. Otelbaev, A criterion for the resolvent of a Sturm-Liouville operator to be kernel. Mathematical notes of the Academy of Sciences of the USSR. 25/4 (1979), 569--572. Cerca con Google

15) P.I. Lizorkin, M. Otelbaev, Embedding theorems and compactness for spaces of Sobolev type with weights. II. Mathematics sbornik of the USSR. 112(154)/1(5) (1981), 56--85. Cerca con Google

16) L.K. Kussainova, "Estimates of embedding widths of weighted spaces" Candidate's dissertation on manuscript copyright). Alma-Ata, 1981. Cerca con Google

17) R. Oinarov, On weighted norm inequalities with three weights. J. London Math. Soc. 48/1 (1993), 137-151. Cerca con Google

18) L.K. Kussainova, Embedding theorems of the Sobolev type anisotropic weighted spaces. I. Izv. VUZov. Mathematics. 11 (1987), 20--31. Cerca con Google

19) E. Smailov, Difference embedding theorem for Sobolev spaces with weight and their application. Reports of the USSR Academy of Sciences. 270/1 (1983), 212--217. Cerca con Google

20) M.S. Aitenova, L.K. Kussainova, On the asymptotics of the distribution of approximation numbers of embeddings of weighted Sobolev classes. I. Math. J. 2/1 (2002), 3--9. Cerca con Google

21) M.S. Aitenova, L.K. Kussainova, On the asymptotics of the distribution of approximation numbers of embeddings of weighted Sobolev classes. II. Math. J. 2/2 (2002), 7--14. Cerca con Google

22) Elias M. Stein, "Sungular integrals and differentiability properties of functions". Princeton University Press, Princeton, New Jersey, 1970. Cerca con Google

23) L.K. Kussainova, "Embedding and interpolation theorems of weighted Sobolev spaces" (Dissertation on manuscript copyright). Karaganda, 1998 (The library of Steklov Mathematical Institute of Russian Academy of sciences, Moscow). Cerca con Google

24) Yu.D. Burago, V.A. Zalgaller, "Geometric inequalities". Nauka, Leningrad, 1980. Cerca con Google

25) L.K. Kussainova, On multipliers in weghted Sobolev spaces. Cerca con Google

Math. col. 196/8 (2005), 21--48. Cerca con Google

26) Z. Karsybayeva, A. Myrzagaliyeva, On the boundedness of a differential operator in Sobolev spaces (rus). Vestnik of the Eurasian National University. 4 (2014) (ISSN 1028-9364). Cerca con Google

27) L. Kussainova, A. Myrzagaliyeva, On the boundedness of a differential operator in spaces of multipliers (rus). Proceedings of the Twelfth International Kazan Summer School-Conference. 51 (2015), 275-276 (ISBN 978-5-9690-0255-5). Cerca con Google

28) A. Myrzagaliyeva, On the boundedness of one dimensional differential operators in weighted Sobolev spaces (rus). Cerca con Google

Vestnik of the Eurasian National University. 109/6 (2015), 29-36 (ISSN 1028-9364). Cerca con Google

29) L. Kussainova, A. Myrzagaliyeva, Ya.T. Sultanaev, On the boundedness of the Schrodinger operator in weighted Sobolev spaces (rus).} Math. notes (2016) (accepted for publication). Cerca con Google

30) A. Myrzagaliyeva, On differential operators and multipliers in weighted Sobolev spaces. PrePrint: Seminario Dottorato 2014/2015, University of Padova (2015), 80-89. Cerca con Google

31) S.M. Nikolskii, "Approximation of functions of several variables and embedding theorems". Nauka, Moscow, 1977. Cerca con Google

32) H. Triebel, "Interpolation theory. Function spaces. Differential operators". Veb Deutscher Verlag, Berlin, 1978. Cerca con Google

33) V.G. Maz'ya, "S.L. Sobolev spaces". LSU, Leningrad, 1985. Cerca con Google

34) M. Guzman, "Differentiation of integrals in R^n". Springer-Verlag, Berlin, 1975. Cerca con Google

35) L.K. Kussainova, On embedding the weighted space W_p^l(Omega;epsilon) to the space L_p(Omega;omega). Math. col. 2 (2000), 132--148. Cerca con Google

36) E. Dyn'kin, B. Osilenker, Weighted estimates for singular integrals and their applications. Results of science and tehn. Ser. Mat. anal. 21 (1983), 42--129. Cerca con Google

37) L.V. Kantorovich, G.P. Akilov, "Functional analysis". Nauka, Moscow, 1984. Cerca con Google

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