Differential expressions with mixed homogeneity and spaces of smooth functions they generate in arbitrary dimension

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Differential expressions with mixed homogeneity and spaces of smooth functions they generate in arbitrary dimension. / Kislyakov, S.V.; Maksimov, D.V.; Stolyarov, D.M.

In: Journal of Functional Analysis, No. 10, 2015, p. 3220-3263.

Research output: Contribution to journal › Article

BibTeX

@article{260a89379507435f8a0d6c2687bbd4fe,

title = "Differential expressions with mixed homogeneity and spaces of smooth functions they generate in arbitrary dimension",

abstract = "{\textcopyright} 2015 Elsevier Inc.Let {T1, . . ., TJ} be a collection of differential operators with constant coefficients on the torus Tn. Consider the Banach space X of functions f on the torus for which all functions Tjf, j=1, . . ., J, are continuous. Extending the previous work of the first two authors, we analyze the embeddability of X into some space C(K) as a complemented subspace. We prove the following. Fix some pattern of mixed homogeneity and extract the senior homogeneous parts (relative to the pattern chosen) {σ1, . . ., σJ} from the initial operators {T1, . . ., TJ}. Let K be the dimension of the linear span of {σ1, . . ., σJ}. If K≥2, then X is not isomorphic to a complemented subspace of C(K) for any compact space K.The main ingredient of the proof of this fact is a new anisotropic embedding theorem of Sobolev type for vector fields.",

author = "S.V. Kislyakov and D.V. Maksimov and D.M. Stolyarov",

year = "2015",

doi = "10.1016/j.jfa.2015.09.001",

language = "English",

pages = "3220--3263",

journal = "Journal of Functional Analysis",

issn = "0022-1236",

publisher = "Elsevier",

number = "10",

}

RIS

TY - JOUR

T1 - Differential expressions with mixed homogeneity and spaces of smooth functions they generate in arbitrary dimension

AU - Kislyakov, S.V.

AU - Maksimov, D.V.

AU - Stolyarov, D.M.

PY - 2015

Y1 - 2015

N2 - © 2015 Elsevier Inc.Let {T1, . . ., TJ} be a collection of differential operators with constant coefficients on the torus Tn. Consider the Banach space X of functions f on the torus for which all functions Tjf, j=1, . . ., J, are continuous. Extending the previous work of the first two authors, we analyze the embeddability of X into some space C(K) as a complemented subspace. We prove the following. Fix some pattern of mixed homogeneity and extract the senior homogeneous parts (relative to the pattern chosen) {σ1, . . ., σJ} from the initial operators {T1, . . ., TJ}. Let K be the dimension of the linear span of {σ1, . . ., σJ}. If K≥2, then X is not isomorphic to a complemented subspace of C(K) for any compact space K.The main ingredient of the proof of this fact is a new anisotropic embedding theorem of Sobolev type for vector fields.

AB - © 2015 Elsevier Inc.Let {T1, . . ., TJ} be a collection of differential operators with constant coefficients on the torus Tn. Consider the Banach space X of functions f on the torus for which all functions Tjf, j=1, . . ., J, are continuous. Extending the previous work of the first two authors, we analyze the embeddability of X into some space C(K) as a complemented subspace. We prove the following. Fix some pattern of mixed homogeneity and extract the senior homogeneous parts (relative to the pattern chosen) {σ1, . . ., σJ} from the initial operators {T1, . . ., TJ}. Let K be the dimension of the linear span of {σ1, . . ., σJ}. If K≥2, then X is not isomorphic to a complemented subspace of C(K) for any compact space K.The main ingredient of the proof of this fact is a new anisotropic embedding theorem of Sobolev type for vector fields.

U2 - 10.1016/j.jfa.2015.09.001

DO - 10.1016/j.jfa.2015.09.001

M3 - Article

SP - 3220

EP - 3263

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 10

ER -

ID: 4013819