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Abstract

In this paper we establish the boundedness of commutators of sublinear operators in weighted grand Morrey spaces. The sublinear operators under consideration contain integral operators such as Hardy-Littlewood and fractional maximal operators, Calderón-Zygmund operators, potential operators etc. The operators and spaces are defined on quasi-metric measure spaces with doubling measure.

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] G uliyev , V. S. , A liyev , S.S. , K araman , T. and S hukurov , P. , Boundedness of sublinear operators and commutators on generalized Morrey spaces , Integral Equations and Operator Theory , 71 ( 3 ) ( 2011 ), 327 – 355

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Abstract  

For two distinct primes p, q, we describe those clones on a set of size pq that contain a given group operation and all constant operations. We show that each such clone is determined by congruences and commutator relations. Thus we obtain that there is only a finite number of such clones on a fixed set.

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Abstract

It is shown that if N(R) is a Lie ideal of R (respectively Jordan ideal and R is 2-torsion-free), then N(R) is an ideal. Also, it is presented a characterization of Noetherian NR rings with central idempotents (respectively with the commutative set of nilpotent elements, the Abelian unit group, the commutative commutator set).

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Abstract  

Let G be a homogeneous group. In this paper, the authors establish several general theorems for the boundedness of sublinear operators and commutators generated by linear operators and BMO(G) functions on the weighted Lebesgue space on G. The conditions of these theorems are satisfied by many important operators in analysis and these operators satisfy only some weak conditions on the size of operators and are known to be bounded in the unweighted case. Some of these theorems are best possible even when G is the Euclidean space. The authors also give some applications of their theorems to the boundedness on weighted spaces of rough singular integrals, oscillatory integrals, parabolic singular integrals, their commutators and the maximal operators associated with them.

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, 2011 . [15] B. A. F . Wehrfritz . On the fixed-point set and commutator subgroup of an automorphism of a group of finite rank . Rend. Sem. Mat. Univ. Padova , 127 : 249 – 255 , 2012 . [16] B. A. F . Wehrfritz . On the fixed-point set of an

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related to Schrödinger operators , J. Math. Anal. Appl ., 373 ( 2011 ), 563 – 579 . [5] Bongioanni , B ., Harboure , E . and Salinas , O . , Weighted inequalities for commutators of Schrödinger-Riesz transforms , J. Math. Anal. Appl ., 392

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