Anno Accademico 2021/2022

  • Docente: Loredana Lanzani
  • Crediti formativi: 6
  • SSD: MAT/05
  • Lingua di insegnamento: Inglese
  • Modalità didattica: Convenzionale - Lezioni in presenza
  • Campus: Bologna
  • Corso: Laurea Magistrale in Matematica (cod. 5827)

Conoscenze e abilità da conseguire

At the end of the course, the student has a knowledge of some basic features and methods of real and harmonic analysis.


Topics covered include: Interpolation of Lebesgue spaces; Fourier coefficients; Hilbert and Riesz transforms; homogeneous singular integrals; Calderon-Zygmund decompositions. Time permitting, vector-valued singular integrals. 


We will use the following textbook:

Loukas Grafakos, ``Classical Fourier Analysis'', 3d Edition (2014), Springer Graduate Texts in Mathematics v. 249.

Metodi didattici

In-class lectures on the theory along with exercises, examples and applications, also aimed to students in the applied curriculum.

This course is taught in English; however,  students enrolled in the regular master program (not the international master) may choose to take the oral exam in Italian. During class, students who wish to ask a question may choose to do so in Italian.

Modalità di verifica e valutazione dell'apprendimento

The evaluation is based on an oral examination that starts with the discussion of a topic chosen by the student among the topics covered during the course. The student will then answer questions pertaining to the proof of theorems that were demonstrated during lecture; the solution of exercises shown in class by the professor, or assigned by the professor as practice problems; the discussion of examples shown in class by the professor, or assigned by the professor as supplemental reading.

Students may choose to take the oral exam in Italian.

Strumenti a supporto della didattica

Prerequisites for this course includes the following topics, which were covered in the ``Analisi Superiore'' component of the ``ANALISI SUPERIORE E GEOMETRIA DIFFERENZIALE'' course taught by Prof. Lanzani in Fall 2021, and can be reviewed in the following chapters in the textbook: Section 2.2 (Schwartz class & Fourier Transform); Section 2.3 (Tempered Distributions); Section 2.4.1 (Distributions supported at a point).

Orario di ricevimento

Consulta il sito web di Loredana Lanzani