Pointwise multipliers between weighted copson and cesàro function spaces

Abstract

In this paper the solution of the pointwise multiplier problem between weighted Copson function spaces Cop p 1 ,q 1 (u 1 , v 1 ) and weighted Cesàro function spaces Ces p 2 ,q 2 (u 2 , v 2 ) is presented, where p 1 , p 2 , q 1 , q 2 ∈ (0, ∞), p 2 ≤ q 2 and u 1 , u 2 , v 1 , v 2 are weights on (0, ∞).2010 Mathematics Subject Classification. Primary 26D10; Secondary 26D15.

Weighted inequalities involving Hardy and Copson operators

“…If 0 < r ≤ q < p < 1, an equivalent condition for the case (vi) of Theorem 2.1, improved in a sense, is available. This result will be particularly handy for future applications, for instance to obtaining a characterization of multipliers between Cesàro and Copson spaces (for partial result in this direction see [22]).…”

“…[38]. Using the characterizations of the inequality (1.1), pointwise multipliers between Cop p 1 ,q 1 (u 1 , v 1 ) and Ces p 2 ,q 2 (u 2 , v 2 ) are given in [22], but again only when p 2 ≤ q 2 . The crucial idea in our new approach is to seek a more manageable version of (1.1).…”

Embeddings between weighted Tandori and Cesàro function spaces

“…Note that the characterization of inequality ( 9) is given in [8]. In the next theorem, we provide a modi…ed version of [8, Theorem 3.1], using the gluing lemmas presented in the recent paper [10]. Denote by…”

“…Recently, in [9] the two sided estimates for the best constant in (1) is given for four weights and four parameters 0 < p 1 ; p 2 ; q 1 ; q 2 < 1 under the restriction p 2 q 2 . Moreover, 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.…”

Another approach to weighted inequalities for a superposition of Copson and Hardy operators

“…We pronounce that the characterizations of inequalities (1.1) -(1.4) are important because many inequalities for classical operators can be reduced to them. These inequalities play an important role in the theory of weighted Morrey-type spaces and Cesàro function spaces (see [5], [11], [12] and [13]). Note that using characterizations of weighted Hardy inequalities it is easy to obtain the characterization of the boundedness of bilinear Hardy-type inequalities (see, for instance, [18] and [1]).…”