Pith Number

pith:L32P4KAH

pith:2026:L32P4KAHYIZPQ3HTSBKSY56VLC

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The nonlinear estimates on quantum Besov spaces

Deyu Chen, Guixiang Hong

Superposition operators with non-smooth symbols are bounded on quantum Besov spaces.

arxiv:2601.11934 v2 · 2026-01-17 · math.FA · math.AP

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Record completeness

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Claims

C1strongest claim

We investigate the boundedness estimates of superposition operators with non-smooth symbols on quantum Besov spaces... As a byproduct, we prove the equivalence of the two descriptions of quantum Besov spaces, resolving the conjecture proposed in [Remark 3.16]{McNLE}.

C2weakest assumption

The non-smooth symbols still satisfy the minimal regularity needed for the novel quantum chain rule and nonlinear interpolation to apply without additional restrictions that would limit the claimed generality.

C3one line summary

Boundedness of superposition operators with non-smooth symbols is established on quantum Besov spaces, together with equivalence of two space descriptions that resolves a prior conjecture.

References

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[1] W. Arendt, C. Batty, M. Hieber and F. Neubrander. Vector-Valued Laplace Transforms and Cauchy Problems. Second edition, Monogr. Math., V ol. 96, Birkh¨auser/Springer, Basel AG, Basel, 2011, MR2798103. 2011

[2] J. Appell and P. P. Zabrejko. Nonlinear superposition operators. V ol. 95 ofCambridge Tracts in Mathematics, Cambridge University Press, Cambridge, 1990. 3 1990

[3] N. A. Azamov, A. L. Carey, P. G. Dodds, and F. A. Sukochev. Operator Integrals, Spectral Shift, and Spectral Flow.Canad. J. Math.,61(2009), no.2, 241–263. 6, 20, 21, 23, 25, 27 2009

[4] S. Bartels. Numerical Methods for Nonlinear Partial Differential Equations. Deutschland: Springer International Publishing, (2015). 3 2015

[5] K. Bamba, M. Saitou and A. Sugamoto. Hydrodynamics on non commutative space: A step toward hydrodynam- ics of granular materials.Prog. Theor. Exp. Phys.,10(2014), 103B03. 2 THE NONLINEAR ESTIMATES ON 2014

Formal links

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Receipt and verification

First computed	2026-05-18T02:44:31.913428Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5ef4fe2807c232f86cf390552c77d5588ba9b9116ec4619715e9f55243d863e1

Aliases

arxiv: 2601.11934 · arxiv_version: 2601.11934v2 · doi: 10.48550/arxiv.2601.11934 · pith_short_12: L32P4KAHYIZP · pith_short_16: L32P4KAHYIZPQ3HT · pith_short_8: L32P4KAH

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/L32P4KAHYIZPQ3HTSBKSY56VLC \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 5ef4fe2807c232f86cf390552c77d5588ba9b9116ec4619715e9f55243d863e1

Canonical record JSON

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    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2026-01-17T06:48:17Z",
    "title_canon_sha256": "65cd3e2bd23ba2d94915bedebc3cb572e0a1e7468150b81e329097a781af5c76"
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