Abstract
In this paper, we study the quantitative weighted bounds for the q-variational singular integral operators with rough kernels, a stronger nonlinearity than the maximal truncations. The main result is for the truncated singular integrals itself
∥Vq {TΩ,ε} ε>0∥Lp(w)→Lp(w) ≲ ∥Ω∥L∞(w)1+1/qAp {w} Ap,
it is the best known quantitative result for this class of operators. In the course of establishing the above estimate, we obtain several quantitative weighted bounds which are of independent interest.
∥Vq {TΩ,ε} ε>0∥Lp(w)→Lp(w) ≲ ∥Ω∥L∞(w)1+1/qAp {w} Ap,
it is the best known quantitative result for this class of operators. In the course of establishing the above estimate, we obtain several quantitative weighted bounds which are of independent interest.
| Original language | English |
|---|---|
| Article number | 31 |
| Pages (from-to) | 1-50 |
| Number of pages | 50 |
| Journal | Journal of Fourier Analysis and Applications |
| Volume | 29 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - Jun 2023 |
Keywords
- Variation inequality
- Singular integral operator
- Quantitative weighted bounds
- Rough kernel