A polynomial Carleson operator along the paraboloid
نویسندگان
چکیده
منابع مشابه
On Stein’s Conjecture on the Polynomial Carleson Operator
We prove that the generalized Carleson operator Cd with polynomial phase function is of strong type (p, r), 1 < r < p < ∞; this yields a positive answer in the 1 < p < 2 case to a conjecture of Stein which asserts that for 1 < p < ∞ we have that Cd is of strong type (p, p). A key ingredient in this proof is the further extension of the relational time-frequency perspective (introduced in [5]) t...
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We prove L(w) bounds for the Carleson operator C, its lacunary version Clac, and its analogue for the Walsh series W in terms of the Aq constants [w]Aq for 1 q p. In particular, we show that, exactly as for the Hilbert transform, ‖C‖Lp(w) is bounded linearly by [w]Aq for 1 q < p. We also obtain L(w) bounds in terms of [w]Ap , whose sharpness is related to certain conjectures (for instance, of K...
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ژورنال
عنوان ژورنال: Revista Matemática Iberoamericana
سال: 2019
ISSN: 0213-2230
DOI: 10.4171/rmi/1057