Abstract
We characterize the weights for which the two-operator inequality ∥ ∥ ∥ ( ∫ x 0 f ( t ) p v ( t ) p d t ) 1 p ∥ ∥ ∥ q , u , ( 0 , ∞ ) ≤ c ∥ ∥ ∥ e s s sup t ∈ ( x , ∞ ) f ( t ) ∥ ∥ ∥ r , w , ( 0 , ∞ ) ‖(∫0xf(t)pv(t)pdt)1p‖q,u,(0,∞)≤c‖esssupt∈(x,∞)f(t)‖r,w,(0,∞) holds for all non-negative measurable functions on ( 0 , ∞ ) (0,∞) , where 0 < p < q ≤ ∞ 0<p<q≤∞ and 0 < r < ∞ 0<r<∞ , namely, we find the least constants in the embeddings between weighted Tandori and Ces\`{a}ro function spaces. We use the combination of duality arguments for weighted Lebesgue spaces and weighted Tandori spaces with weighted estimates for the iterated integral operators.
Highlights
Given two function spaces X, Y and an operator T, a standard problem is characterizing the conditions for which T maps X into Y
We shall begin with the de...nitions of the function spaces considered in this paper
In [9] the two sided estimates for the best constant in (1) is given for four weights and four parameters 0 < p1; p2; q1; q2 < 1 under the restriction p2 q2. Using these results, in [9, Theorems 3.11-3.12], the associate spaces of weighted Copson and Cesàro function spaces were characterized and in [10] pointwise multipliers between Cesàro and Copson function spaces are given for some ranges of parameters
Summary
Given two function spaces X, Y and an operator T, a standard problem is characterizing the conditions for which T maps X into Y. In [6], inequality (1) is considered for two di¤erent parameters in the special case p1 = p2 = 1, q1 = p, q2 = q, v1(t) = t 1, v2(t) = 1, u1(t)p = v(t), u2(t)q = w(t)t q, t > 0, under the restriction q 1 in order to characterize the embeddings between some Lorentz-type spaces. In [9] the two sided estimates for the best constant in (1) is given for four weights and four parameters 0 < p1; p2; q1; q2 < 1 under the restriction p2 q2 Using these results, in [9, Theorems 3.11-3.12], the associate spaces of weighted Copson and Cesàro function spaces were characterized and in [10] pointwise multipliers between Cesàro and Copson function spaces are given for some ranges of parameters. In the last section, we give the proofs of our main results
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
