On Fourier $M^{q}_{p}$ multiplier criteria of Marcinkiewicz type
نویسندگان
چکیده
منابع مشابه
0 Endpoint Multiplier Theorems of Marcinkiewicz Type
We establish sharp (H 1 , L 1,q) and local (L log r L, L 1,q) mapping properties for rough one-dimensional multipliers. In particular, we show that the multipliers in the Marcinkiewicz multiplier theorem map H 1 to L 1,∞ and L log 1/2 L to L 1,∞ , and that these estimates are sharp.
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Let A be a function with derivatives of order m and DγA∈ Λ̇β (0 < β < 1, |γ| =m). The authors in the paper proved that ifΩ∈ Ls(Sn−1) (s≥ n/(n−β)) is homogeneous of degree zero and satisfies a vanishing condition, then both the higher-order Marcinkiewicz-type integral μΩ and its variation μ̃ A Ω are bounded from L p(Rn) to Lq(Rn) and from L1(Rn) to Ln/(n−β),∞(Rn), where 1 < p < n/β and 1/q = 1/p− ...
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ژورنال
عنوان ژورنال: Studia Mathematica
سال: 1976
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm-58-1-7-19