Sobolev inequalities with variable exponent attaining the values 1 and n
P. Harjulehto, P. Hästö (2008)
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P. Harjulehto, P. Hästö (2008)
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Petteri Harjulehto, Juha Kinnunen (2004)
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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.
Amiran Gogatishvili, Júlio S. Neves, Bohumír Opic (2005)
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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.
Dmitryi V. Prokhorov (2004)
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In the paper we obtain a precise characterization of Hardy type inequalities with weights for the negative indices and the indices between 0 and 1 and establish a duality between these cases.
S. Hencl (2008)
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Oliver Dragicevic, Loukas Grafakos, María Cristina Pereyra, Stefanie Petermichl (2005)
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Amiran Gogatishvili, Lubos Pick (2003)
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Daniele Debertol (2005)
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Nguyen Quang Dieu (2006)
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We generalize classical results for plurisubharmonic functions and hyperconvex domain to q-plurisubharmonic functions and q-hyperconvex domains. We show, among other things, that B-regular domains are q-hyperconvex. Moreover, some smoothing results for q-plurisubharmonic functions are also given.
A. Clop, D. Faraco, J. Mateu, J. Orobitg, X. Zhong (2009)
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S. Antontsev, S. Shmarev (2009)
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