Grand Lebesgue Spaces norm estimates for multivariate functional operations

E. Ostrovsky; L. Sirota

RECORD

Grand Lebesgue Spaces norm estimates for multivariate functional operations

E. Ostrovsky, L. Sirota

Functional Analysis · Submitted 5 May 2018

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We will show also the strong or at last weak (i.e. up to multiplicative constant) exactness of obtained estimates.

how it is stated · asserted 0.94 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,281 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.30 · human participants 0.03 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.14 · compares with prior results 0.05 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We intend to derive the moment and exponential tail estimates for the so-called bivariate or more generally multivariate functional operations, not necessary to be linear or even multilinear. We will show also the strong or at last weak (i.e. up to multiplicative constant) exactness of obtained estimates.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We intend to derive the moment and exponential tail estimates for the so-called bivariate or more generally multivariate functional operations, not necessary to be linear or even multilinear.	contribution 0.74	0.36	0.16	asserted 0.59
s1	We will show also the strong or at last weak (i.e. up to multiplicative constant) exactness of obtained estimates.	result 0.62	0.72	0.32	asserted 0.94

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

We intend to derive the moment and exponential tail estimates for the so-called bivariate or more generally multivariate functional operations, not necessary to be linear or even multilinear. We will show also the strong or at last weak (i.e. up to multiplicative constant) exactness of obtained estimates.

Human review

How Pith checks papers → · Full audit of this paper →

How the literature uses it

2 arXiv papers cite this in 2 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.