Abstract
The authors prove that the parametrized area integral and function are bounded from the weighted weak Hardy space to the weighted weak Lebesgue space as satisfies a class of the integral Dini condition, respectively.
Highlights
Introduction and Main ResultsSuppose that Ω ∈ L1(Sn−1) is homogeneous of degree zero on Rn and satisfies∫ Ω (x) dσ (x) = 0, (1)Sn−1 where Sn−1 denotes the unit sphere of Rn (n ⩾ 2) equipped with normalized Lebesgue measure dσ = dσ(x), x = x/|x|, x ≠ 0
We will introduce some notations and preliminary lemmas used in the proofs of our main theorems
Lmfe(exma)smubreaalob5nleg(ssfuetenoc[Wt1i9oH]n)wsp. ({LRfeknt()x,0)t}h
Summary
In 2007, Ding et al [12, 13] gave the boundedness of the parametrized area integral μΩρ ,S and gλ∗ function μλ∗,ρ on the Hardy space and weak Hardy space when Ω satisfies a class of the integral Dini conditions. Abstract and Applied Analysis obtained the boundedness on the weighted Hardy space for the parametrized Littlewood-Paley operators with Ω satisfying the logarithmic type Lipschitz conditions. Inspired by the results mentioned previously, in this paper, we will study the boundedness of the parametrized area integral μΩρ ,S and gλ∗ function μλ∗,ρ on the weighted weak Hardy spaces. In 2000, Quek and Yang introduced the weighted weak Hardy spaces WHwp(Rn) in [19] and established their atomic decompositions. Weighted weak Hardy space is defined by WHwp(Rn) = {f ∈ S(Rn) : Gwf ∈ WLpw(Rn)}.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
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 call
