zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
On boundedness of a certain class of Hardy-Steklov type operators in Lebesgue spaces. (English) Zbl 1193.26013
Suppose that $w$ and $v$ are locally integrable non-negative weight functions. The paper under review studies $L_p$-$L_q$ boundedness of the Hardy-Steklov type operator $\mathcal{K}$ defined by $$ \mathcal{K}f(x)=w(x)\int_{a(x)}^{b(x)}k(x,y)f(y)v(y)dy, $$ where the border functions $a(x)$ and $b(x)$ are differentiable and strictly increasing on $(0,\infty)$, $a(0)=b(0)=0$, $a(x)<b(x)$ for $x\in (0,\infty)$, $a(\infty)=b(\infty)=\infty$, and the kernel $k(x,y)$ is strictly positive on the set $\{(x,y):x>0,a(x)<y<b(x)\}$ and satisfies at least one of two generalized Oinarov’s conditions $\mathcal{O}_b$ and $\mathcal{O}_a$.

26D10Inequalities involving derivatives, differential and integral operators
26D15Inequalities for sums, series and integrals of real functions
26D07Inequalities involving other types of real functions
Full Text: EMIS EuDML