Currently displaying 1 – 8 of 8

Showing per page

Order by Relevance | Title | Year of publication

Essential norm estimates for multilinear singular and fractional integrals

Alexander Meskhi — 2019

Commentationes Mathematicae

We derive lower two-weight estimates for the essential norm (measure of noncompactness) for multilinear Hilbert and Riesz transforms, and Riesz potential operators in Banach function lattices. As a corollary we have appropriate results in weighted Lebesgue spaces. From these statements we conclude that there is no ( m + 1 ) -tuple of weights ( v , w 1 , , w m ) for which these operators are compact from L w 1 p 1 × × L w m p m to L v q .

Trace inequalities for fractional integrals in grand Lebesgue spaces

Vakhtang KokilashviliAlexander Meskhi — 2012

Studia Mathematica

rning the boundedness for fractional maximal and potential operators defined on quasi-metric measure spaces from L p ) , θ ( X , μ ) to L q ) , q θ / p ( X , ν ) (trace inequality), where 1 < p < q < ∞, θ > 0 and μ satisfies the doubling condition in X. The results are new even for Euclidean spaces. For example, from our general results D. Adams-type necessary and sufficient conditions guaranteeing the trace inequality for fractional maximal functions and potentials defined on so-called s-sets in ℝⁿ follow. Trace inequalities...

One-weight weak type estimates for fractional and singular integrals in grand Lebesgue spaces

Vakhtang KokilashviliAlexander Meskhi — 2014

Banach Center Publications

We investigate weak type estimates for maximal functions, fractional and singular integrals in grand Lebesgue spaces. In particular, we show that for the one-weight weak type inequality it is necessary and sufficient that a weight function belongs to the appropriate Muckenhoupt class. The same problem is discussed for strong maximal functions, potentials and singular integrals with product kernels.

Boundedness of commutators of singular and potential operators in generalized grand Morrey spaces and some applications

Vakhtang KokilashviliAlexander MeskhiHumberto Rafeiro — 2013

Studia Mathematica

In the setting of spaces of homogeneous type, it is shown that the commutator of Calderón-Zygmund type operators as well as the commutator of a potential operator with a BMO function are bounded in a generalized grand Morrey space. Interior estimates for solutions of elliptic equations are also given in the framework of generalized grand Morrey spaces.

Page 1

Download Results (CSV)