VOLUME 3, 2012 NUMBER 3http://repository.enu.kz:8080/handle/data/106302020-06-03T19:27:17Z2020-06-03T19:27:17ZOMTSA 2011http://repository.enu.kz:8080/handle/data/107772013-06-26T09:09:21Z2013-06-26T00:00:00ZOMTSA 2011
2013-06-26T00:00:00ZTo the 70th birthday of Professor V.I. Burenkovhttp://repository.enu.kz:8080/handle/data/107762013-06-26T09:07:56Z2013-06-26T00:00:00ZTo the 70th birthday of Professor V.I. Burenkov
2013-06-26T00:00:00ZRECENT PROGRESS IN STUDYING THE BOUNDEDNESS OF CLASSICAL OPERATORS OF REAL ANALYSIS IN GENERAL MORREY-TYPE SPACES. IV.I. Burenkovhttp://repository.enu.kz:8080/handle/data/107752013-06-26T09:03:06Z2013-06-26T00:00:00ZRECENT PROGRESS IN STUDYING THE BOUNDEDNESS OF CLASSICAL OPERATORS OF REAL ANALYSIS IN GENERAL MORREY-TYPE SPACES. I
V.I. Burenkov
The survey is aimed at providing detailed information about recent results
in the problem of the boundedness in general Morrey-type spaces of various important
operators of real analysis, namely of the maximal operator, fractional maximal
operator, Riesz potential, singular integral operator, Hardy operator. The main focus
is on the results which contain, for a certain range of the numerical parameters,
necessary and sufficient conditions on the functional parameters characterizing general
Morrey-type spaces, ensuring the boundedness of the aforementioned operators from
one general Morrey-type space to another one. The major part of the survey is dedicated
to the results obtained by the author jointly with his co-authores A. Gogatishvili,
M.L. Goldman, H.V. Guliyev, V.S. Guliyev, P. Jain, R. Mustafaev, E.D. Nursultanov,
R. Oinarov, A. Serbetci, T.V. Tararykova. Part I of the survey contains discussion of
the definition and basic properties of the local and global general Morrey-type spaces,
of embedding theorems, and of the boundedness properties of the maximal operator.
Part II of the survey will contain discussion of boundedness properties of the fractional
maximal operator, Riesz potential, singular integral operator, commutators of singular
integral operator, Hardy operator. It will also contain discussion of interpolation
theorems, of methods of proofs and of open problems.
2013-06-26T00:00:00Z