The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “ L p inequalities for the growth of polynomials with restricted zeros”

On the topology of polynomials with bounded integer coefficients

De-Jun Feng (2016)

Journal of the European Mathematical Society

Similarity:

For a real number q > 1 and a positive integer m , let Y m ( q ) : = i = 0 n ϵ i q i : ϵ i 0 , ± 1 , ... , ± m , n = 0 , 1 , ... . In this paper, we show that Y m ( q ) is dense in if and only if q < m + 1 and q is not a Pisot number. This completes several previous results and answers an open question raised by Erdös, Joó and Komornik [8].

On square functions associated to sectorial operators

Christian Le Merdy (2004)

Bulletin de la Société Mathématique de France

Similarity:

We give new results on square functions x F = 0 F ( t A ) x 2 d t t 1 / 2 p associated to a sectorial operator A on L p for 1 &lt; p &lt; . Under the assumption that A is actually R -sectorial, we prove equivalences of the form K - 1 x G x F K x G for suitable functions F , G . We also show that A has a bounded H functional calculus with respect to . F . Then we apply our results to the study of conditions under which we have an estimate ( 0 | C e - t A ( x ) | 2 d t ) 1 / 2 q M x p , when - A generates a bounded semigroup e - t A on L p and C : D ( A ) L q is a linear mapping.

Geometric rigidity of × m invariant measures

Michael Hochman (2012)

Journal of the European Mathematical Society

Similarity:

Let μ be a probability measure on [ 0 , 1 ] which is invariant and ergodic for T a ( x ) = a x 𝚖𝚘𝚍 1 , and 0 < 𝚍𝚒𝚖 μ < 1 . Let f be a local diffeomorphism on some open set. We show that if E and ( f μ ) E μ E , then f ' ( x ) ± a r : r at μ -a.e. point x f - 1 E . In particular, if g is a piecewise-analytic map preserving μ then there is an open g -invariant set U containing supp μ such that g U is piecewise-linear with slopes which are rational powers of a . In a similar vein, for μ as above, if b is another integer and a , b are not powers of a common integer, and if ν is...

Coppersmith-Rivlin type inequalities and the order of vanishing of polynomials at 1

(2016)

Acta Arithmetica

Similarity:

For n ∈ ℕ, L > 0, and p ≥ 1 let κ p ( n , L ) be the largest possible value of k for which there is a polynomial P ≢ 0 of the form P ( x ) = j = 0 n a j x j , | a 0 | L ( j = 1 n | a j | p ) 1 / p , a j , such that ( x - 1 ) k divides P(x). For n ∈ ℕ, L > 0, and q ≥ 1 let μ q ( n , L ) be the smallest value of k for which there is a polynomial Q of degree k with complex coefficients such that | Q ( 0 ) | > 1 / L ( j = 1 n | Q ( j ) | q ) 1 / q . We find the size of κ p ( n , L ) and μ q ( n , L ) for all n ∈ ℕ, L > 0, and 1 ≤ p,q ≤ ∞. The result about μ ( n , L ) is due to Coppersmith and Rivlin, but our proof is completely different and much shorter even...

The multiplicity of the zero at 1 of polynomials with constrained coefficients

Peter Borwein, Tamás Erdélyi, Géza Kós (2013)

Acta Arithmetica

Similarity:

For n ∈ ℕ, L > 0, and p ≥ 1 let κ p ( n , L ) be the largest possible value of k for which there is a polynomial P ≠ 0 of the form P ( x ) = j = 0 n a j x j , | a 0 | L ( j = 1 n | a j | p 1/p , aj ∈ ℂ , such that ( x - 1 ) k divides P(x). For n ∈ ℕ and L > 0 let κ ( n , L ) be the largest possible value of k for which there is a polynomial P ≠ 0 of the form P ( x ) = j = 0 n a j x j , | a 0 | L m a x 1 j n | a j | , a j , such that ( x - 1 ) k divides P(x). We prove that there are absolute constants c₁ > 0 and c₂ > 0 such that c 1 ( n / L ) - 1 κ ( n , L ) c 2 ( n / L ) for every L ≥ 1. This complements an earlier result of the authors valid for every n ∈ ℕ and L ∈...

A Hardy type inequality for W 0 m , 1 ( Ω ) functions

Hernán Castro, Juan Dávila, Hui Wang (2013)

Journal of the European Mathematical Society

Similarity:

We consider functions u W 0 m , 1 ( Ω ) , where Ω N is a smooth bounded domain, and m 2 is an integer. For all j 0 , 1 k m - 1 , such that 1 j + k m , we prove that i u ( x ) d ( x ) m - j - k W 0 k , 1 ( Ω ) with k ( i u ( x ) d ( x ) m - j - k ) L 1 ( Ω ) C u W m , 1 ( Ω ) , where d is a smooth positive function which coincides with dist ( x , Ω ) near Ω , and l denotes any partial differential operator of order l .

Commutators of Marcinkiewicz integrals on Herz spaces with variable exponent

Hongbin Wang (2016)

Czechoslovak Mathematical Journal

Similarity:

Let Ω L s ( S n - 1 ) for s 1 be a homogeneous function of degree zero and b a BMO function. The commutator generated by the Marcinkiewicz integral μ Ω and b is defined by [ b , μ Ω ] ( f ) ( x ) = ( 0 | x - y | t Ω ( x - y ) | x - y | n - 1 [ b ( x ) - b ( y ) ] f ( y ) d y | 2 d t t 3 1 / 2 . In this paper, the author proves the ( L p ( · ) ( n ) , L p ( · ) ( n ) ) -boundedness of the Marcinkiewicz integral operator μ Ω and its commutator [ b , μ Ω ] when p ( · ) satisfies some conditions. Moreover, the author obtains the corresponding result about μ Ω and [ b , μ Ω ] on Herz spaces with variable exponent.

A weighted inequality for the Hardy operator involving suprema

Pavla Hofmanová (2016)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Let u be a weight on ( 0 , ) . Assume that u is continuous on ( 0 , ) . Let the operator S u be given at measurable non-negative function ϕ on ( 0 , ) by S u ϕ ( t ) = sup 0 < τ t u ( τ ) ϕ ( τ ) . We characterize weights v , w on ( 0 , ) for which there exists a positive constant C such that the inequality 0 [ S u ϕ ( t ) ] q w ( t ) d t 1 q 0 [ ϕ ( t ) ] p v ( t ) d t 1 p holds for every 0 < p , q < . Such inequalities have been used in the study of optimal Sobolev embeddings and boundedness of certain operators on classical Lorenz spaces.

Neutral set differential equations

Umber Abbas, Vasile Lupulescu, Donald O&amp;#039;Regan, Awais Younus (2015)

Czechoslovak Mathematical Journal

Similarity:

The aim of this paper is to establish an existence and uniqueness result for a class of the set functional differential equations of neutral type D H X ( t ) = F ( t , X t , D H X t ) , X | [ - r , 0 ] = Ψ , where F : [ 0 , b ] × 𝒞 0 × 𝔏 0 1 K c ( E ) is a given function, K c ( E ) is the family of all nonempty compact and convex subsets of a separable Banach space E , 𝒞 0 denotes the space of all continuous set-valued functions X from [ - r , 0 ] into K c ( E ) , 𝔏 0 1 is the space of all integrally bounded set-valued functions X : [ - r , 0 ] K c ( E ) , Ψ 𝒞 0 and D H is the Hukuhara derivative. The continuous dependence of solutions on initial...

Embeddings between weighted Copson and Cesàro function spaces

Amiran Gogatishvili, Rza Mustafayev, Tuğçe Ünver (2017)

Czechoslovak Mathematical Journal

Similarity:

In this paper, characterizations of the embeddings between weighted Copson function spaces Cop p 1 , q 1 ( u 1 , v 1 ) and weighted Cesàro function spaces Ces p 2 , q 2 ( u 2 , v 2 ) are given. In particular, two-sided estimates of the optimal constant c in the inequality d ( 0 0 t f ( τ ) p 2 v 2 ( τ ) d τ q 2 / p 2 u 2 ( t ) d t ) 1 / q 2 c 0 t f ( τ ) p 1 v 1 ( τ ) d τ q 1 / p 1 u 1 ( t ) d t 1 / q 1 , d where p 1 , p 2 , q 1 , q 2 ( 0 , ) , p 2 q 2 and u 1 , u 2 , v 1 , v 2 are weights on ( 0 , ) , are obtained. The most innovative part consists of the fact that possibly different parameters p 1 and p 2 and possibly different inner weights v 1 and v 2 are allowed. The proof is based on the combination of duality techniques...

S -shaped component of nodal solutions for problem involving one-dimension mean curvature operator

Ruyun Ma, Zhiqian He, Xiaoxiao Su (2023)

Czechoslovak Mathematical Journal

Similarity:

Let E = { u C 1 [ 0 , 1 ] : u ( 0 ) = u ( 1 ) = 0 } . Let S k ν with ν = { + , - } denote the set of functions u E which have exactly k - 1 interior nodal zeros in (0, 1) and ν u be positive near 0 . We show the existence of S -shaped connected component of S k ν -solutions of the problem u ' 1 - u ' 2 ' + λ a ( x ) f ( u ) = 0 , x ( 0 , 1 ) , u ( 0 ) = u ( 1 ) = 0 , where λ > 0 is a parameter, a C ( [ 0 , 1 ] , ( 0 , ) ) . We determine the intervals of parameter λ in which the above problem has one, two or three S k ν -solutions. The proofs of the main results are based upon the bifurcation technique.

The norm of the polynomial truncation operator on the unit disk and on [-1,1]

Tamás Erdélyi (2001)

Colloquium Mathematicae

Similarity:

Let D and ∂D denote the open unit disk and the unit circle of the complex plane, respectively. We denote by ₙ (resp. c ) the set of all polynomials of degree at most n with real (resp. complex) coefficients. We define the truncation operators Sₙ for polynomials P c of the form P ( z ) : = j = 0 n a j z j , a j C , by S ( P ) ( z ) : = j = 0 n a ̃ j z j , a ̃ j : = a j | a j | m i n | a j | , 1 (here 0/0 is interpreted as 1). We define the norms of the truncation operators by S , D r e a l : = s u p P ( m a x z D | S ( P ) ( z ) | ) / ( m a x z D | P ( z ) | ) , S , D c o m p : = s u p P c ( m a x z D | S ( P ) ( z ) | ) / ( m a x z D | P ( z ) | . Our main theorem establishes the right order of magnitude of the above norms: there is an absolute constant c₁...

A Diophantine inequality with four squares and one k th power of primes

Quanwu Mu, Minhui Zhu, Ping Li (2019)

Czechoslovak Mathematical Journal

Similarity:

Let k 5 be an odd integer and η be any given real number. We prove that if λ 1 , λ 2 , λ 3 , λ 4 , μ are nonzero real numbers, not all of the same sign, and λ 1 / λ 2 is irrational, then for any real number σ with 0 < σ < 1 / ( 8 ϑ ( k ) ) , the inequality | λ 1 p 1 2 + λ 2 p 2 2 + λ 3 p 3 2 + λ 4 p 4 2 + μ p 5 k + η | < max 1 j 5 p j - σ has infinitely many solutions in prime variables p 1 , p 2 , , p 5 , where ϑ ( k ) = 3 × 2 ( k - 5 ) / 2 for k = 5 , 7 , 9 and ϑ ( k ) = [ ( k 2 + 2 k + 5 ) / 8 ] for odd integer k with k 11 . This improves a recent result in W. Ge, T. Wang (2018).