Scientific seminar on functional analysis and its applications under the guidance of A.V. Arutyunov, V.I. Burenkov and M. L. Goldman and V.N. Rozova

Speaker: Prof. V.I. Burenkov (RUDN University)

Topic: Connection of inequalities for a maximal operator in Morrey-type spaces and inequalities for a Hardy operator for monotonically decreasing functions.

The following issues will be considered:

• Maximum operator and its basic properties
• Boundedness in Lebesgue spaces
• Boundedness in Morrey spaces
• Necessary and sufficient conditions of boundedness in general local Morrey-type spaces.
• Hardy operator
• Boundedness in Lebesgue spaces
• Boundedness in Lebesgue spaces on the cone of monotone decreasing functions
• Boundedness on the weighted Lebesgue spaces on the cone of monotone decreasing functions
• Reduction of the problem on the boundedness of the maximal operator to the problem on the boundedness of the Hardy operator in weighted Lebesgue spaces on the cone of monotone decreasing functions