Pith Number

pith:6IQUCOGK

pith:2014:6IQUCOGKU6XW3R5GDSH4FHD3MK

not attested not anchored not stored refs pending

Two weight norm inequalities for fractional integral operators and commutators

David Cruz-Uribe

arxiv:1412.4157 v1 · 2014-12-12 · math.CA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6IQUCOGKU6XW3R5GDSH4FHD3MK}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Cited by

4 papers in Pith

Dyadic fractional Sobolev spaces: Embeddings and algebra property

Multilinear embedding theorem for fractional sparse operators

The Kerman-Sawyer trace theorem for product Morrey spaces

The Adams trace theorem for product Morrey spaces

Receipt and verification

First computed	2026-05-18T02:31:20.061884Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f2214138caa7af6dc7a61c8fc29c7b62b547597ea6578e31c2400a849497983a

Aliases

arxiv: 1412.4157 · arxiv_version: 1412.4157v1 · doi: 10.48550/arxiv.1412.4157 · pith_short_12: 6IQUCOGKU6XW · pith_short_16: 6IQUCOGKU6XW3R5G · pith_short_8: 6IQUCOGK

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/6IQUCOGKU6XW3R5GDSH4FHD3MK \
  | 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: f2214138caa7af6dc7a61c8fc29c7b62b547597ea6578e31c2400a849497983a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a7e74f25cdecf98a5298bb709a5aa52f877893cb737f0087320f6c1fe3066943",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2014-12-12T22:56:41Z",
    "title_canon_sha256": "287e69342eba8477f418563bb04166e9c57e650558fb05590cc192099508a587"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.4157",
    "kind": "arxiv",
    "version": 1
  }
}