function spaces history

The Prague seminar on function spaces

a brief history

The origins of the Prague seminar on function spaces go back to early 1970s when Svatopluk Fučík, Oldřich John and Alois Kufner organized a seminar at the Faculty of Mathematics and Physics of the Charles University. The seminar was run by a rather informal group of mathematicians interested in the study of function spaces and related problems, mainly their use in solving partial differential equations. Later the seminar was transferred to the Mathematical Institute of the Czechoslovak Academy of Sciences. Here the core of the function spaces group was formed by Miroslav Krbec, Alois Kufner (head), Bohumír Opic and Jiří Rákosník. Since the very beginning the seminar was devoted to the rapidly developing topic of function spaces, weighted inequalities, integral operators, embedding theorems, and their aplications in PDEs, Fourier analysis, and harmonic analysis. In the 1980's the seminar attracted the attention of several (then) young mathematicians who eventually wrote their diploma and PhD. theses under the supervision of one of the founders of the seminar and became themselves regular members of the group. This generation included Petr Gurka, Aleš Nekvinda, Luboš Pick and Jan Lang. Since 1990 the seminar has been informally headed by Bohumír Opic.

The activities of the seminar have always been reflecting current advances of the field. Important papers and new monographs have been gone through in detail and vigorously discussed. As a consequence, since the 1990's the topics were enriched of theory of interpolation, spaces with logarithmic smoothness, Hardy-type inequalities of higher order and weighted inequalities for operators acting on monotone functions. Since the outbreak of the 21st century, the topics of research were extended to rearrangement-invariant spaces with focus on their optimality in Sobolev embeddings

In the late 90's the group was joined by Amiran Gogatishvili, originally from Tbilisi, Georgia. The long list of students and young mathematicians who temporarily joined the activities of the seminar during the 2000's and the following decades included David Opěla, Jan Vybíral, Luboš Dostál, Eva Kaspříková, David Pražák, Lukáš Malý, Pavla Hofmanová, Pavel Milar, Eva Pernecká, Filip Soudský, Kristýna Kuncová, Miloslav Holík, Rastislav Oľhava, Martin Křepela, Martin Franců, Vít Musil, Lenka Slavíková, Eva Buriánková, Zdeněk Mihula, Ondřej Bouchala and others.

The members of the seminar are involved in organizing the regular international meetings such as the Spring Schools on Nonlinear Analysis, Function Spaces and Applications (NAFSA - since 1978), international conferences on Function Spaces, Diferential Operators and Nonlinear Analysis (FSDONA - since 1988, jointly with mathematicians from Finland and Germany), or spring schools on Function Spaces and related topics held every two years at Paseky nad Jizerou (since 1999).

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