Displaying similar documents to “Interpolation of Sobolev spaces, Littlewood-Paley inequalities and Riesz transforms on graphs.”

Optimality of embeddings of Bessel-potential-type spaces into generalized Hölder spaces.

Amiran Gogatishvili, Júlio S. Neves, Bohumír Opic (2005)

Publicacions Matemàtiques

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We establish the sharpness of embedding theorems for Bessel-potential spaces modelled upon Lorentz-Karamata spaces and we prove the non-compactness of such embeddings. Target spaces in our embeddings are generalized Hölder spaces. As consequences of our results, we get continuous envelopes of Bessel-potential spaces modelled upon Lorentz-Karamata spaces.

Differentiation bases for Sobolev functions on metric spaces.

Petteri Harjulehto, Juha Kinnunen (2004)

Publicacions Matemàtiques

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We study Lebesgue points for Sobolev functions over other collections of sets than balls. Our main result gives several conditions for a differentiation basis, which characterize the existence of Lebesgue points outside a set of capacity zero.

Carleson's Theorem: proof, complements, variations.

Michael T. Lacey (2004)

Publicacions Matemàtiques

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Carleson's Theorem from 1965 states that the partial Fourier sums of a square integrable function converge pointwise. We prove an equivalent statement on the real line, following the method developed by the author and C. Thiele. This theorem, and the proof presented, is at the center of an emerging theory which complements the statement and proof of Carleson's theorem. An outline of these variations is also given.