Ryskul Oinarov

Criteria of boundedness and compactness of a class of matrix operators

The aim of this article is to obtain criteria of boundedness and compactness for a wide class of matrix operators from one weighted lp,v space of sequences to another weighted lq,u space, in the case 1 < p ≤ q < ∞. We introduce a general class of matrices. Then we establish necessary and sufficient conditions for the boundedness and compactness of the operators (A+f)i:=∑j=1iai,jfj, i ≥ 1 and (A-f)j:=∑i=j∞ai,jfi, j ≥ 1 corresponding to matrices in such classes by using the method of localization. Our classes are more general than those for which corresponding Hardy inequalities are known in the literature.2010 Mathematics Subject Classification: 26D15; 47B37.

Boundedness of -Multiple Discrete Hardy Operators with Weights for

We find necessary and sufficient conditions on weighted sequences , , , and , for which the operator is bounded from to for .

Hardy-type inequalities in fractional h-discrete calculus

AbstractThe first power weighted version of Hardy’s inequality can be rewritten as ∫0∞(xα−1∫0x1tαf(t)dt)pdx≤[pp−α−1]p∫0∞fp(x)dx,f≥0,p≥1,α<p−1,

Some New Hardy-type Integral Inequalities on Cones of Monotone Functions

\int _{0}^{\infty } \biggl( x^{\alpha -1} \int _{0}^{x} \frac{1}{t ^{\alpha }}f(t)\,dt \biggr) ^{p}\,dx\leq \biggl[ \frac{p}{p-\alpha -1} \biggr] ^{p} \int _{0}^{\infty }f^{p}(x)\,dx,\quad f\geq 0,p\geq 1, \alpha < p-1,

On Hardy q-inequalities

where the constant C=[pp−α−1]p

Weighted inequalities for a class of matrix operators : the case of p≤q

C= [ \frac{p}{p-\alpha -1} ] ^{p}

Weighted inequalities of Hardy type for matrix operators: The case qlp

is sharp. This inequality holds in the reversed direction when 0≤p<1

Reversion of Hölder type inequalities for sums of weighted norms and additive weighted estimates of integral operators

0\leq p<1