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

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Abstract (italian or 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 (a different language)

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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