Pseudodifferential operators on Bochner spaces and an application

Pierre Portal; Željko Štrkalj

doi:10.1007/s00209-006-0934-x

Pseudodifferential operators on Bochner spaces and an application

Pierre Portal^*
, Željko Štrkalj

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

28 Citations (Scopus)

Abstract

We consider pseudodifferential operators with operator valued symbols a(x,ξ) acting on a UMD Banach space X. Assuming some regularity of Hölder type in x and Mihlin type in ξ we prove L _p (ℝⁿ ;X) boundedness of such operators. This result is then applied to the study of L _p -maximal regularity for nonautonomous parabolic evolution equations.

Original language	English
Pages (from-to)	805-819
Number of pages	15
Journal	Mathematische Zeitschrift
Volume	253
Issue number	4
DOIs	https://doi.org/10.1007/s00209-006-0934-x
Publication status	Published - Aug 2006

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title = "Pseudodifferential operators on Bochner spaces and an application",

abstract = "We consider pseudodifferential operators with operator valued symbols a(x,ξ) acting on a UMD Banach space X. Assuming some regularity of H{\"o}lder type in x and Mihlin type in ξ we prove L p (ℝn ;X) boundedness of such operators. This result is then applied to the study of L p -maximal regularity for nonautonomous parabolic evolution equations.",

author = "Pierre Portal and {\v Z}eljko {\v S}trkalj",

year = "2006",

month = aug,

doi = "10.1007/s00209-006-0934-x",

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T1 - Pseudodifferential operators on Bochner spaces and an application

AU - Portal, Pierre

AU - Štrkalj, Željko

PY - 2006/8

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N2 - We consider pseudodifferential operators with operator valued symbols a(x,ξ) acting on a UMD Banach space X. Assuming some regularity of Hölder type in x and Mihlin type in ξ we prove L p (ℝn ;X) boundedness of such operators. This result is then applied to the study of L p -maximal regularity for nonautonomous parabolic evolution equations.

AB - We consider pseudodifferential operators with operator valued symbols a(x,ξ) acting on a UMD Banach space X. Assuming some regularity of Hölder type in x and Mihlin type in ξ we prove L p (ℝn ;X) boundedness of such operators. This result is then applied to the study of L p -maximal regularity for nonautonomous parabolic evolution equations.

UR - https://www.scopus.com/pages/publications/33744779115

U2 - 10.1007/s00209-006-0934-x

DO - 10.1007/s00209-006-0934-x

M3 - Article

SN - 0025-5874

VL - 253

SP - 805

EP - 819

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 4

ER -

Pseudodifferential operators on Bochner spaces and an application

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