PreprintCC BY 4.0arXiv
On the pullback on spaces of distributions with prescribed microregularity with respect to a general Banach space
Abstract
We consider the space 𝒟'EL(U) of all distributions on the open set U whose wave front set measured with respect to a Banach space E lies in a closed conic subset L of U×(ℝnbackslash{0}). The Banach space E only satisfies mild technical assumptions. We show that the pullback by a diffeomorphism f:O→ U is a topological isomorphism f*:𝒟'EL(U)→𝒟'Ef*L(O). In the case when E is the Lp-Sobolev space Wr,p(ℝn) of order r∈ℝ, we study the pullback by a smooth map f:O→ U of constant rank.
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BibTeX
@misc{pilipovic2026pullback,
title = {{On the pullback on spaces of distributions with prescribed microregularity with respect to a general Banach space}},
author = {Stevan Pilipović and Bojan Prangoski and Stefan Tutić},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08741},
eprint = {2609.08741},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08741},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the pullback on spaces of distributions with prescribed microregularity with respect to a general Banach space
AU - Stevan Pilipović
AU - Bojan Prangoski
AU - Stefan Tutić
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08741
UR - https://arxiv.org/abs/2609.08741
AB - We consider the space 𝒟'^E_L(U) of all distributions on the open set U whose wave front set measured with respect to a Banach space E lies in a closed conic subset L of U×(ℝ^nbackslash{0}). The Banach space E only satisfies mild technical assumptions. We show that the pullback by a diffeomorphism f:O→ U is a topological isomorphism f^*:𝒟'^E_L(U)→𝒟'^E_f^*L(O). In the case when E is the L^p-Sobolev space W^r,p(ℝ^n) of order r∈ℝ, we study the pullback by a smooth map f:O→ U of constant rank.
ER -