Marcinkiewicz integrals with rough kernel associated with Schrӧdinger
operators and commutators on generalized vanishing local Morrey spaces
F. Gürbüz
Let L=Δ+V(x) be a Schrӧdinger operator, where
Δ is the Laplacian on R^{n}, while nonnegative potential
V(x) belonging to the reverse Hӧlder class. In this
paper, using the some conditions on
φ( x.r), we dwell on
the boundedness of Marcinkiewicz integrals with rough kernel associated with
schrӧ}dinger operators and commutators generated by these operators and
local Campanato functions both on generalized local Morrey spaces and on
generalized vanishing local Morrey spaces, respectively. As an application of
the above results, the boundedness of parametric Marcinkiewicz integral and
its commutator both on generalized local Morrey spaces and on generalized
vanishing local Morrey spaces is also obtained.
Tbilisi Mathematical Journal, Vol. 11(3) (2018), pp. 133156
