scholarly journals A note on two-weight inequalities for multiple Hardy-type operators

2005 ◽  
Vol 3 (3) ◽  
pp. 223-237 ◽  
Author(s):  
Alexander Meskhi
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Hardy Type ◽  
Right Hand ◽  
The Right ◽  
Necessary And Sufficient ◽  
Hardy Type Operators

Necessary and sufficient conditions on a pair of weights guaranteeing two-weight estimates for the multiple Riemann-Liouville transforms are established provided that the weight on the right-hand side satisfies some additional conditions.

scholarly journals Potential Operators on Cones of Nonincreasing Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-26 ◽  
Author(s):  
Alexander Meskhi ◽  
Ghulam Murtaza
Keyword(s):  
Mixed Type ◽  
Sufficient Conditions ◽  
Product Type ◽  
Necessary And Sufficient Conditions ◽  
Lebesgue Spaces ◽  
Potential Operators ◽  
Right Hand ◽  
The Right ◽  
Necessary And Sufficient

Necessary and sufficient conditions on weight pairs guaranteeing the two-weight inequalities for the potential operators(Iαf)(x)=∫0∞(f(t)/|x−t|1−α)dtand(ℐα1,α2f)(x,y)=∫0∞∫0∞(f(t,τ)/|x−t|1−α1|y−τ|1−α2)dtdτon the cone of nonincreasing functions are derived. In the case ofℐα1,α2, we assume that the right-hand side weight is of product type. The same problem for other mixed-type double potential operators is also studied. Exponents of the Lebesgue spaces are assumed to be between 1 and ∞.

scholarly journals Weighted norm inequalities and indices

2006 ◽  
Vol 4 (1) ◽  
pp. 43-71 ◽  
Author(s):  
Joaquim Martín ◽  
Mario Milman
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Weighted Norm ◽  
Weighted Norm Inequalities ◽  
Norm Inequalities ◽  
Rearrangement Invariant Spaces ◽  
Hardy Type ◽  
Necessary And Sufficient ◽  
Invariant Spaces ◽  
Hardy Type Operators

We extend and simplify several classical results on weighted norm inequalities for classical operators acting on rearrangement invariant spaces using the theory of indices. As an application we obtain necessary and sufficient conditions for generalized Hardy type operators to be bounded on?p(w),?p,8(w),Gp(w)andGp,8(w).

Moment Problems and Quasi-Hausdorff Transformations

1968 ◽  
Vol 11 (2) ◽  
pp. 225-236 ◽  
Author(s):  
Dany Leviatan
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Complex Numbers ◽  
Moment Problems ◽  
Right Hand ◽  
The Right ◽  
Necessary And Sufficient

The sequence to sequence quasi - Hausdorff transformations were defined by Hardy [1] 1 1. 19 p. 277 as follows. For a given sequence {μn} (n ≥ 0) of real or complex numbers, define the operator Δ by for k > l. {tm} (m ≥ 0) is called the sequence to sequence quasi-Hausdorff transform by means of {μn} (or, in short, the [QH, μn] transform) of {sn} (n ≥ 0) if if , provided that the sums on the right-hand side converge for all m ≥ 0. Ramanujan in [11] and [12] has defined the series to series quasi-Hausdorff transformation s and has proved necessary and sufficient conditions for the regularity of the two kinds of transformations.

Semicritical Rings and the Quotient Problem

1984 ◽  
Vol 27 (2) ◽  
pp. 160-170
Author(s):  
Karl A. Kosler
Keyword(s):  
Quotient Ring ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Prime Ideals ◽  
Regular Elements ◽  
The Right ◽  
Minimal Prime ◽  
Necessary And Sufficient ◽  
Quotient Rings ◽  
The Relationship

AbstractThe purpose of this paper is to examine the relationship between the quotient problem for right noetherian nonsingular rings and the quotient problem for semicritical rings. It is shown that a right noetherian nonsingular ring R has an artinian classical quotient ring iff certain semicritical factor rings R/Ki, i = 1,…,n, possess artinian classical quotient rings and regular elements in R/Ki lift to regular elements of R for all i. If R is a two sided noetherian nonsingular ring, then the existence of an artinian classical quotient ring is equivalent to each R/Ki possessing an artinian classical quotient ring and the right Krull primes of R consisting of minimal prime ideals. If R is also weakly right ideal invariant, then the former condition is redundant. Necessary and sufficient conditions are found for a nonsingular semicritical ring to have an artinian classical quotient ring.

On the Ring of Quotients at a Prime Ideal of a Right Noetherian Ring

1972 ◽  
Vol 24 (4) ◽  
pp. 703-712 ◽  
Author(s):  
A. G. Heinicke
Keyword(s):  
Prime Ideal ◽  
Noetherian Ring ◽  
Quotient Ring ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Torsion Class ◽  
Ring Of Quotients ◽  
Ore Condition ◽  
The Right ◽  
Necessary And Sufficient

J. Lambek and G. Michler [3] have initiated the study of a ring of quotients RP associated with a two-sided prime ideal P in a right noetherian ring R. The ring RP is the quotient ring (in the sense of [1]) associated with the hereditary torsion class τ consisting of all right R-modules M for which HomR(M, ER(R/P)) = 0, where ER(X) is the injective hull of the R-module X.In the present paper, we shall study further the properties of the ring RP. The main results are Theorems 4.3 and 4.6. Theorem 4.3 gives necessary and sufficient conditions for the torsion class associated with P to have property (T), as well as some properties of RP when these conditions are indeed satisfied, while Theorem 4.6 gives necessary and sufficient conditions for R to satisfy the right Ore condition with respect to (P).

Reconstruction of a convolution operator from the right-hand side on the semiaxis

2015 ◽  
Vol 23 (5) ◽  
Author(s):  
Anatoly F. Voronin
Keyword(s):  
Inverse Problem ◽  
Integral Operator ◽  
Sufficient Conditions ◽  
Stability Theorem ◽  
Explicit Formulas ◽  
Right Hand ◽  
The Right ◽  
Necessary And Sufficient ◽  
Operator Kernel ◽  
Problem Solvability

AbstractIn this paper, a Volterra integral equation of the first kind in convolutions on the semiaxis when the integral operator kernel and the right-hand side of the equation have a bounded support is considered. An inverse problem of reconstructing the solution to the equation and the integral operator kernel from values of the right-hand side is formulated. Necessary and sufficient conditions for the inverse problem solvability are obtained. A uniqueness and stability theorem is proved. Explicit formulas for reconstruction of the solution and kernel are obtained.

Study of Semi-projective Retractable Modules

2007 ◽  
Vol 14 (03) ◽  
pp. 489-496 ◽  
Author(s):  
A. Haghany ◽  
M. R. Vedadi
Keyword(s):  
Endomorphism Ring ◽  
Semiprime Ring ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Singular Ideal ◽  
The Right ◽  
Necessary And Sufficient

For a semi-projective retractable module MR with endomorphism ring S, we prove u.dim MR= u.dim SS, and find necessary and sufficient conditions on M in order that S be respectively semiprime, right nonsingular, finitely cogenerated, cocyclic, or weakly co-Hopfian. Precise descriptions of the right singular ideal of S and the socle of M are given, and in addition if S is a semiprime ring, it is shown that MR is FI-extending if and only if SS is FI-extending.

scholarly journals Characterizations of weighted dynamic Hardy-type inequalities with higher-order derivatives

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
S. H. Saker ◽  
R. R. Mahmoud ◽  
K. R. Abdo
Keyword(s):  
Time Scales ◽  
Sufficient Conditions ◽  
Type Inequality ◽  
Higher Order ◽  
Necessary And Sufficient Conditions ◽  
Hardy Type Inequality ◽  
Hardy Type Inequalities ◽  
Hardy Type ◽  
Weighted Functions ◽  
Necessary And Sufficient

AbstractIn this paper, we establish some necessary and sufficient conditions for the validity of a generalized dynamic Hardy-type inequality with higher-order derivatives with two different weighted functions on time scales. The corresponding continuous and discrete cases are captured when $\mathbb{T=R}$ T = R and $\mathbb{T=N}$ T = N , respectively. Finally, some applications to our main result are added to conclude some continuous results known in the literature and some other discrete results which are essentially new.

Right Bol Quasi-Fields

1969 ◽  
Vol 21 ◽  
pp. 1409-1420
Author(s):  
Michael J. Kallaher
Keyword(s):  
Division Ring ◽  
Near Field ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Image Position ◽  
The Right ◽  
Necessary And Sufficient ◽  
Bol Loops

We shall consider quasi-fields which satisfy the multiplicative Identity1.1(1.1) will be called the right Bol law and a quasi-field satisfying it will be called a right Bol quasi-held. Moufang quasi-fields, i.e., those satisfying the Moufang identity1.2were studied in (5). Quasi-fields satisfying the left Bol identity1.3were studied by Burn (3) and the author (6). Such quasi-fields are called Bol quasi-fields.Our investigation will parallel the investigations in (5; 6). In § 2 we derive necessary and sufficient conditions for a right Bol quasi-field to be an alternative division ring and also criteria for it to be a near-field. With this information we derive in §§ 3 and 4 new characterizations of Moufang planes similar to those in (5; 6).Loops satisfying (1.1) have been studied by Robinson (10). He calls such loops Bol loops.

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