Real interpolation for families of Banach spaces (II).
Convergence a.e. of spherical partial Fourier integrals on weighted spaces for radial functions: endpoint estimates
We prove some extrapolation results for operators bounded on radial functions with p ∈ (p₀,p₁) and deduce some endpoint estimates. We apply our results to prove the almost everywhere convergence of the spherical partial Fourier integrals and to obtain estimates on maximal Bochner-Riesz type operators acting on radial functions in several weighted spaces.
Endpoint estimates from restricted rearrangement inequalities.
Extrapolation theory for the real interpolation method.
We develop an abstract extrapolation theory for the real interpolation method that covers and improves the most recent versions of the celebrated theorems of Yano and Zygmund. As a consequence of our method, we give new endpoint estimates of the embedding Sobolev theorem for an arbitrary domain Omega.
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