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1

Mixed norms and Sobolev type inequalities

100%

Kolyada V.

Banach Center Publications

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2006

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tom 72

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nr 1

141-160

EN

We study mixed norm spaces that arise in connection with embeddings of Sobolev and Besov spaces. We prove Sobolev type inequalities in terms of these mixed norms. Applying these results, we obtain optimal constants in embedding theorems for anisotropic Besov spaces. This gives an extension of the estimate proved by Bourgain, Brezis and Mironescu for isotropic Besov spaces.

2

On limiting embeddings of Besov spaces

63%

Kolyada V., Lerner A.

Studia Mathematica

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2005

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tom 171

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nr 1

1-13

EN

We investigate the classical embedding $B_{p,θ}^{s} ⊂ B_{q,θ}^{s-n(1/p-1/q)}$. The sharp asymptotic behaviour as s → 1 of the operator norm of this embedding is found. In particular, our result yields a refinement of the Bourgain, Brezis and Mironescu theorem concerning an analogous problem for the Sobolev-type embedding. We also give a different, elementary proof of the latter theorem.

3

A transplantation theorem for ultraspherical polynomials at critical index

63%

Guadalupe J., Kolyada V.

Studia Mathematica

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2001

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tom 147

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nr 1

51-72

EN

We investigate the behaviour of Fourier coefficients with respect to the system of ultraspherical polynomials. This leads us to the study of the "boundary" Lorentz space $ℒ_{λ}$ corresponding to the left endpoint of the mean convergence interval. The ultraspherical coefficients ${cₙ^{(λ)}(f)}$ of $ℒ_{λ}$-functions turn out to behave like the Fourier coefficients of functions in the real Hardy space ReH¹. Namely, we prove that for any $f ∈ ℒ_{λ}$ the series $∑_{n=1}^{∞} cₙ^{(λ)}(f) cos nθ $ is the Fourier series of some function φ ∈ ReH¹ with $||φ||_{ReH¹} ≤ c||f||_{ℒ_{λ}}$.

Ograniczanie wyników

2 Studia Mathematica

1 Banach Center Publications

3 Kolyada V.

1 Guadalupe J.

1 Lerner A.

1 2006

1 2005

1 2001

Mixed norms and Sobolev type inequalities

On limiting embeddings of Besov spaces

A transplantation theorem for ultraspherical polynomials at critical index