[Turkmath:7060] Weekly Online Seminar "Analysis and Applied Mathematics"

[Allaberen Ashyralyev]

Dear All,
You are cordially invited to the  Weekly Online Seminar “Analysis and
Applied Mathematics” on
*Date*: Tuesday, March 11, 2025
*Time:* 13.00-14.00 (Istanbul) = 12.00-13.00 (Ghent) = 15.00-16.00 (Almaty)
*Place:* Zoom link:
https://us02web.zoom.us/j/6678270445?pwd=SFNmQUIvT0tRaHlDaVYrN3l5bzJVQT09,
Conference ID: 667 827 0445, Access code: 1

*Speaker:  Academician**,*Prof. Dr. Alexander *Meskhi Kutaisi International
University and TSU A. Razmadze Mathematical Institute,Georgia*
*Title: * *Multilinear fractional integrals: boundedness criteria and sharp
estimates*
*Abstract:* Necessary and sufficient conditions on a measure μ guaranteeing
the boundedness of the multilinear fractional integral operator Tγ,μ

(mm) (defined with respect to a measure μ) from the product of Lorentz
spaces ∏ Lμ m rk,sk k=1 to the Lorentz space Lμ p,q(X) are derived. The
results are new even for
linear fractional integrals Tγ,μ (i.e., for m = 1). From the general
results we obtain a criterion for the validity of the Sobolev inequality
for Tγ,μ(m) in Lorentz spaces defined with respect to μ. We investigate

the same problem for Morrey-Lorentz spaces. Sharp form for the Olsen’s
inequality in multilinear setting is obtained. Criteria for the
bound-edness of multilinear Riesz potential operator from Lebesgue space to
a Lebesgue space with weight will be presented.Finally, weighted criteria
for the boundedness of m− linear Riemann-Liouville operators will be also
discussed.Talk is based on the papers [1]–[5].
References:
[1] L. Grafakos and A. Meskhi, On sharp Olsen’s and trace inequalities for
multilinear fractional
integrals, Potential Analysis 59 (2023), 1039-1050.
[2] V. Kokilashvili, M. Mastylo and A. Meskhi, On the Boundedness of
Multilinear Fractional
Integral Operators, J. Geome. Anal. 30 (2020), 667-679.
[3] V. Kokilashvili and A. Meskhi, Fractional integrals on measure spaces,
Fract. Calc. Appl.
Anal. 4 (2001), No.1, 1–24.
[4] A. Meskhi and L. Natelashvili, Boundedness criteria for linear and
multilinear fractional
integral operators in Lorentz spaces, Trans. A. Razmadze Math. Inst. 178
(2024), No. 2, 331-333.
[5] A. Meskhi and L. Natelashvili, Boundedness criteria for linear and
multilinear fractional
integral operators in Lorentz spaces (to appear).
 *Abstracts and forthcoming talks can be found on our webpage*
https://sites.google.com/view/aam-seminars
With my best wishes
*Prof. Dr. Allaberen Ashyralyev *
*Department of Mathematics, Bahcesehir University,**34349**, Istanbul,
Turkiye*
*Peoples' Friendship University of Russia (RUDN University),** Ul Miklukho
Maklaya 6, Moscow 117198, Russian Federation *
*Institute of Mathematics and Mathematical Modelling, 050010, Almaty,
Kazakhstan*
*e-mail: allaberen.ashyralyev at bau.edu.tr
<allaberen.ashyralyev at neu.edu.tr> and **aallaberen at gmail.com
<aallaberen at gmail.com> *
 http://akademik.bahcesehir.edu.tr/web/allaberenashyralyev

https://sites.google.com/view/aam-seminars

https://ejaam.org/editorial.html

*https://icaam-online.org/ <https://icaam-online.org/>*

*https://www.genealogy.math.ndsu.nodak.edu/id.php?id=95872&fChrono=1
<https://www.genealogy.math.ndsu.nodak.edu/id.php?id=95872&fChrono=1>*
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