Embeddings between weighted Tandori and Cesàro function spaces

Abstract

We characterize the weights for which the two-operator inequality $$\Vert ({\int }_0^{x}f\left(t{)}^{p}v\right(t{)}^{p}dt{)}^{\frac{1}{p}}{\Vert }_{q,u,(0,\infty )}\le c\Vert ess\underset{t\in (x,\infty )}{sup}f\left(t\right){\Vert }_{r,w,(0,\infty )}$$ holds for all non-negative measurable functions on $(0,\infty )$, where $0<p<q\le \infty$ and $0<r<\infty$, 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.

Keywords

• Cesàro function spaces
• Copson function spaces
• Tandori function spaces
• embeddings
• weighted inequalities
• Hardy operator
• Copson operator
• iterated operators

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