Azerbaijan National Academy of Science

Topic of  PhD thesis:

-         specialty code

-         specialty name

-         topic name

01.01.02 

Differential Equations 

Integral operators of potential type on spaces of homogeneous type and their applications to differential equations

Total number of printed scientific publications:

-          number of scientific publications printed abroad:

-          number of papers  published in journals indexed and abstracted in international databases

28

20

 17 

Staff training:     

-         number of  PhD

2

The characterization  of  some  new  iterated  Hardy-type inequalities;

The characterization  of  the  actions  of classical operators of Real and Harmonic Analysis - maximal, singular and potential operators - in  Morrey-type  spaces;

The characterization of the equivalence of norms in generalized Morrey spaces of the fractional maximal operator and Riesz potential;

The characterizations of dual and pre-dual spaces of local and global Morrey-type spaces;

Weak type estimates in classical Morrey spaces for maximal commutators and commutators of maximal functions;

1. A. Gogatishvili, R.Ch. Mustafayev, A Note on Boundedness of the Hardy-Littlewood Maximal Operator on Morrey Spaces, Mediterr. J. Math. 13 (4) (2016), 1885--1891. MR3530905

2. R.Ch. Mustafayev, T. Ünver, Reverse Hardy-type inequalities for supremal operators with measures, Math. Inequal. & Appl. 18 (4) (2015), 1295--1311. MR3414598

3. R.Ch. Mustafayev, T. Ünver, Embeddings between weighted local Morrey-type spaces and weighted Lebesgue spaces, J. of Math. Inequal. 9 (1) (2015), 277--296. MR3333923

4. M. Agcayazi, A. Gogatishvili, K. Koca, R.Ch. Mustafayev, A note on maximal commutators and commutators of maximal functions,} J. Math. Soc. Japan. 67 (2) (2015), 581--593. MR3340187

5. V.S. Guliyev, T. Karaman, R.Ch. Mustafayev, A. Serbetci, Commutators of sublinear operators generated by Calderon-Zygmund operator on generalized weighted Morrey spaces, Czechoslovak Math. J. 64 (139) (2014), 365--385. MR3277742

6. A.Gogatishvili, R.Ch. Mustafayev, L.-E.~Persson, Some new iterated Hardy-type inequalities: the case θ =1, J. Inequal. Appl. (2013), 29 pp. MR3320124

7. A. Gogatishvili, R.Ch. Mustafayev, New characterization of Morrey spaces, Eurasian Math. J. 4 (1) (2013), 54--64. MR3118891

8. A. Gogatishvili, R.Ch. Mustafayev, New pre-dual space of Morrey space, J. Math. Anal. Appl. 397 (2) (2013), 678--692. MR2979604

9. A. Gogatishvili, R.Ch. Mustafayev, L.-E. Persson, Some new iterated Hardy-type inequalities, J. Funct. Spaces Appl. 2012, 30 pp. MR3000818

10. A. Akbulut, V.S. Guliyev, R.Ch. Mustafayev, On the Boundedness of the maximal operator and singular integral operators in generalized Morrey spaces, Math. Bohem. 137 (1) (2012), 27--43. MR2978444

11. R.Ch. Mustafayev, On boundedness of sublinear operators in weighted Morrey spaces, Azerb. J. Math. 2 (1) (2012), 63--75. MR2967285

12. A. Gogatishvili, R.Ch. Mustafayev, Multidimensional reverse Hardy inequalities, Math. Inequal. & Appl. 15 (1) (2012), 1--14. MR2919426

13. A. Gogatishvili, R.Ch. Mustafayev, Equivalence of norms of Riesz potential and fractional maximal function in generalized Morrey spaces, Collect. Math. 63 (1) 2012, 11--28. MR2887108

14. V.S. Guliyev, R.Ch.Mustafayev, Boundedness of the anisotropic maximal and anisotropic singular integral operators in generalized Morrey spaces, Acta Math. Sin. (Engl. Ser.) 27 (12) (2011), 2361--2370. MR2853794

15. A. Gogatishvili, R.Ch. Mustafayev, Dual spaces of local Morrey-type spaces, Czechoslovak Math. J. 61 (136) (2011), 609--622. MR2853078

16. A. Gogatishvili, R.Ch. Mustafayev, On a theorem of Muchenhoupt-Wheeden in generalized Morrey spaces, Eurasian Math. J. 2 (2) (2011), 134--138. MR2910836

17. V.I. Burenkov, A. Gogatishvili, V.S. Guliyev, R.Ch. Mustafayev, Sufficient conditions for boundedness of the Riesz potential in local Morrey-type spaces, Potential Anal. 35 (2011), 67--87. MR2804553

18. V.S. Guliyev, R.Ch. Mustafayev, A. Serbetci, Stein-Weiss inequalities for the fractional integral operators in Carnot groups and applications, Complex Var. Elliptic Equ. 55 (8-10) (2010), 847--863. MR2674868

19. V.I. Burenkov, A. Gogatishvili, V.S. Guliyev, R.Ch. Mustafayev, Boundedness of the fractional maximal operator in local Morrey-type spaces, Complex Var. Elliptic Equ. 55 (8-10) (2010), 739--758. MR2674862

Institute of Mathematics and Mechanics ANAS, AZ1141, Azerbaijan Republic, Baku, B.Vahabzade, 9

(+994 12) 5390102 

rzamustafayev@gmail.com