Estimates of rearrangements and imbedding theorems. (English. Russian original) Zbl 0693.46030

Kolyada, V. I.

Math. USSR, Sb. 64, No. 1, 1-21 (1989); translation from Mat. Sb., Nov. Ser. 136(178), No. 1(5), 3-23 (1988).

In the paper the author obtains estimates of rearrangements in terms of integral smoothness. The author uses this estimates to prove embedding theorems.

Reviewer: St.Wedrychowicz

MSC:

46E30	Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46E35	Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
26A15	Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable
26A16	Lipschitz (Hölder) classes
30D55	\(H^p\)-classes (MSC2000)

Keywords:

\(L^ p\)-modulus of continuity; Orlicz classes \(\phi(L)\); Sobolev and Hardy-Littlewood theorems; estimates of rearrangements in terms of integral smoothness; embedding theorems