Estimates for operators in mixed weighted 𝐿^{𝑝}-spaces

Heinig, Hans P.

doi:10.1090/S0002-9947-1985-0768721-5

Estimates for operators in mixed weighted $L\sp p$ -spaces

Author: Hans P. Heinig
Journal: Trans. Amer. Math. Soc. 287 (1985), 483-493
MSC: Primary 42B10; Secondary 44A10, 46M35, 47B38
DOI: https://doi.org/10.1090/S0002-9947-1985-0768721-5
MathSciNet review: 768721
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Abstract: A weighted Marcinkiewicz interpolation theorem is proved. If is simultaneously of weak type $({p_i},{q_i})$ , ; $1 \leqslant {p_0} < {p_1} \leqslant \infty$ and , certain weight functions, then is bounded from to for , $p \geqslant 1$ . The result is applied to obtain weighted estimates for the Laplace and Fourier transform, as well as the Riesz potential.

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