Naslov
Sharp L^p estimates of powers of the complex Riesz transform

Autori
Carbonaro, Andrea ; Dragičević, Oliver ; Kovač, Vjekoslav

Izvornik
Mathematische Annalen (0025-5831) 386 (2023); 1081-1125

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
complex Hilbert transform ; singular integral ; kernel estimation ; sharp estimate

Sažetak
Let R_{; ; 1, 2}; ; be scalar Riesz transforms on R^2. We prove that the L^p norms of k-th powers of the operator R_2+iR_1 behave exactly as |k|^{; ; 1−2/p}; ; *p, uniformly in k∈Z∖{; ; 0}; ; , p≥2. This gives a complete asymptotic answer to a question suggested by Iwaniec and Martin in 1996. The main novelty are the lower estimates, of which we give three different proofs. We also conjecture the exact value of ∥(R_2+iR_1)^k∥_p. Furthermore, we establish the sharp behaviour of weak (1, 1) constants of (R_2+iR_1)^k and an L^∞ to BMO estimate that is sharp up to a logarithmic factor.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA