Grand and small norms in Lebesgue spaces
Copyright policy )Grand and small norms in Lebesgue spaces
We present a new approach to the definition of grand and small Lebesgue spaces. This in particular allows to include into consideration the extreme exponents and . Basically, the study of the extreme exponent case is the main result of the article. However, we expect that our general construction for the norms in grand and small Lebesgue spaces will imply further studies of the spaces and operators in these spaces in such a general setting.
- Southern Federal University Russian Federation
- Yaroslavl State University Russian Federation
Banach lattices, grand and small Lebesgue spaces, Interpolation between normed linear spaces, extrapolation, symmetric spaces, Inequalities for sums, series and integrals, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Banach lattices, grand and small Lebesgue spaces, Interpolation between normed linear spaces, extrapolation, symmetric spaces, Inequalities for sums, series and integrals, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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