## One Citation

Norm of the discrete Cesàaro operator minus identity

- MathematicsMathematical Inequalities & Applications
- 2022

The norm of C−I on l, where C is the Cesàro operator, is shown to be 1/(p − 1) when 1 < p ≤ 2. This verifies a recent conjecture of G. J. O. Jameson. The norm of C − I on l is also determined when 2…

## References

SHOWING 1-10 OF 25 REFERENCES

On the optimal relationships between LP-norms for the Hardy operator and its dual for decreasing functions

- Computer Science, MathematicsJ. Approx. Theory
- 2020

Sharp inequalities between L p − norms ( 1 p ∞ ) of functions H f and H ∗ f are proved, where H is the Hardy operator, H∗ is its dual, and f is a nonnegative nonincreasing function on ( 0, ∞) .

Averaging operators on decreasing or positive functions: Equivalence and optimal bounds

- Computer Science, MathematicsJ. Approx. Theory
- 2019

Abstract We study the optimal bounds for the Hardy operator S minus the identity, as well as S and its dual operator S ∗ , on the full range 1 ≤ p ≤ ∞ , for the cases of decreasing, positive or…

Maximal functions on classical Lorentz spaces and Hardy’s inequality with weights for nonincreasing functions

- Mathematics
- 1990

A characterization is given of a class of classical Lorentz spaces on which the Hardy Littlewood maximal operator is bounded. This is done by determining the weights for which Hardy's inequality…

Sharp estimates for the identity minus Hardy operator on the cone of decreasing functions

- Mathematics
- 2008

It is shown that if we restrict the identity minus Hardy operator on the cone of nonnegative decreasing functions f in L-p, then we have the sharp estimateparallel to(I - H)f parallel to(Lp) = 2.It…

Ahlfors-Beurling operator on radial functions

- Mathematics
- 2012

We give a simple proof of a sharp bound of Ahlfors--Beurling operator on complex-valued radial functions. In the language of the Calculus of Variation we prove a certain estimates for stretch and…

Sharp inequalities for the Beurling–Ahlfors transform on radial functions

- Mathematics
- 2013

For 1 ≤ p ≤ 2, we prove sharp weak-type (p, p) estimates for the BeurlingAhlfors operator acting on the radial function subspaces of Lp(C). A similar sharp Lp result is proved for 1 < p ≤ 2. The…

The L^p-norms of the Beurling–Ahlfors transform on radial functions

- Mathematics
- 2017

We calculate the norms of the operators connected to the action of the Beurling-Ahlfors transform on radial function subspaces introduced by Ba\~nuelos and Janakiraman. In particular, we find the…

WEIGHTED INEQUALITIES INVOLVING TWO HARDY OPERATORS WITH APPLICATIONS TO EMBEDDINGS OF FUNCTION SPACES

- Mathematics
- 2008

We find necessary and sufficient conditions for the two-operator weighted inequality ¥ R 0 1 t R 0 f(s)ds q w(t)dt 1/q 6C ¥ R 0 ¥ R t f(s) s ds p v(t)dt 1/p . We use this inequality to study…