Convex functions and Orlicz spaces 1000-1M19FWP
Convex functions, Young functions, N-functions and their special classes satisfying typical growth conditions. Young conjugate (Legendre transform, complementary function). Orlicz spaces and their basic functional-analytic properties dependent on the speed of growth of the function defining norm. Extensions of classical inequalities. Sobolev-Orlicz spaces and their basic properties. Embeddings of Sobolev-Orlicz spaces into Orlicz spaces.
Type of course
Learning outcomes
Student
- knows and understands the meaning of growth conditions of convex functions
- knows and understands relations between growth of convex functions and generated by them Orlicz and Orlicz-Sobolev spaces
- knows and can apply basic tools of analysis in Orlicz spaces
- understands embeddings of Sobolev-Orlicz spaces into Orlicz spaces
Assessment criteria
Examination: oral exam or presentation.
Additional information
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes:
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