Two-weight mixed ф-inequalities for the one-sided maximal function

Volume 115 / 1995

Qinsheng Lai Studia Mathematica 115 (1995), 1-22 DOI: 10.4064/sm-115-1-1-22


Suppose u, v, w, and t are weight functions on an appropriate measure space (X,μ), and $Φ_1$, $Φ_2$ are Young functions satisfying a certain relationship. Let T denote an operator to be specified below. The main purpose of this paper is to characterize (i) the strong type mixed Φ-inequality $Φ^{-1}_{2}(ʃ_{X} Φ_{2}(T(fv))wdμ) ≤ Φ^{-1}_{1} (ʃ_X Φ_{1}(Cf)vdμ)$, (ii) the weak type mixed Φ-inequality $Φ^{-1}_2 (ʃ_{|Tf|>λ}$ Φ_{2}(λw)tdμ) ≤ Φ^{-1}_{1} (ʃ_{X} Φ_{1}(Cfu)vdμ)$ and (iii) the extra-weak type mixed Φ-inequality $|{x ∈ X : |Tf(x)| > λ}|_{wdμ} ≤ Φ_{2}Φ^{-1}_{1} (ʃ_{X} Φ_{1}(Cfu/λ)vdμ)$, when T is the one-sided maximal function $M^{+}_{g}$; as well to characterize (iii) for the Fefferman-Stein type fractional maximal operator and the Hardy-type operator.


  • Qinsheng Lai

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image