AbstractLet tn(x) be any real trigonometric polynomial of degree n such that ∥tn∥L∞ ⩽ 1. Here we are concerned with obtaining the best possible upper estimate of ∝02π(tn(k)(x))2r + 2dx∝02π(tn(k)(x))2rdx where r ⩾ 0 (integer). As a special case we obtain (1.2). Let ∥tn∥L2 and ∥tn(r)∥L2 be given where tn is any real trigonometric polynomial. In Theorem 2 we shall obtain the estimate of ∥tn(j)∥L2 in terms of ∥tn∥L2 and ∥tn(r)∥L2. The results are again the best possible
AbstractFor trigonometric polynomials on [-π,π]≡T, the classical Jackson inequality En(f)p⩽Cωr(f,1/n...
AbstractLet Tn be the set of all trigonometric polynomials of degree at most n. Denote by Φ+ the cla...
AbstractThe inequality Tn(xy) ⩽ Tn(x) Tn(y), x, y ⩾ 1, where Tn(x) is the Tchebycheff polynomial of ...
AbstractLet tn(x) be any real trigonometric polynomial of degree n such that ∥tn∥L∞ ⩽ 1. Here we are...
AbstractWe obtain a Remez-type inequality for a trigonometric polynomial Qn of degree at most n with...
AbstractWith the notation K≔R(mod2π),||p||Lλ(K)≔∫K|p(t)|λdt1/λandMλ(p)≔12π∫K|p(t)|λdt1/λwe prove the...
AbstractWe prove the following theorem: Let m≥2 be a given integer and let a,b,c be real numbers. Th...
Abstract. We obtain a sharp Remez inequality for the trigonometric polynomial Tn of degree n on [0, ...
AbstractLet 0<p<∞ and 0⩽α<β⩽2π. We prove that for n⩾1 and trigonometric polynomials sn of degree ⩽n,...
We study sharp estimates of integral functionals for operators on the set T n of real trigonometric ...
AbstractLet 0<p<∞ and 0⩽α<β⩽2π. We prove that for trigonometric polynomials sn of degree ⩽n, we have...
AbstractWe study sharp estimates of integral functionals for operators on the set Tn of real trigono...
AbstractSome inequalities associated with the Laplacian for trigonometric polynomials are given, whi...
AbstractThe sequence of extremal problems In = sup{(2π)−1 ∝02π¦p(θ)¦2 dθ¦pϵ Pn}, where Pn denotes th...
AbstractThe well-known Marcinkiewicz-Zygmund inequality ∫02x|T(x)|pdx1p⩽Ap1n∑k=02nT2kπ2n+1p1p, 1<p<+...
AbstractFor trigonometric polynomials on [-π,π]≡T, the classical Jackson inequality En(f)p⩽Cωr(f,1/n...
AbstractLet Tn be the set of all trigonometric polynomials of degree at most n. Denote by Φ+ the cla...
AbstractThe inequality Tn(xy) ⩽ Tn(x) Tn(y), x, y ⩾ 1, where Tn(x) is the Tchebycheff polynomial of ...
AbstractLet tn(x) be any real trigonometric polynomial of degree n such that ∥tn∥L∞ ⩽ 1. Here we are...
AbstractWe obtain a Remez-type inequality for a trigonometric polynomial Qn of degree at most n with...
AbstractWith the notation K≔R(mod2π),||p||Lλ(K)≔∫K|p(t)|λdt1/λandMλ(p)≔12π∫K|p(t)|λdt1/λwe prove the...
AbstractWe prove the following theorem: Let m≥2 be a given integer and let a,b,c be real numbers. Th...
Abstract. We obtain a sharp Remez inequality for the trigonometric polynomial Tn of degree n on [0, ...
AbstractLet 0<p<∞ and 0⩽α<β⩽2π. We prove that for n⩾1 and trigonometric polynomials sn of degree ⩽n,...
We study sharp estimates of integral functionals for operators on the set T n of real trigonometric ...
AbstractLet 0<p<∞ and 0⩽α<β⩽2π. We prove that for trigonometric polynomials sn of degree ⩽n, we have...
AbstractWe study sharp estimates of integral functionals for operators on the set Tn of real trigono...
AbstractSome inequalities associated with the Laplacian for trigonometric polynomials are given, whi...
AbstractThe sequence of extremal problems In = sup{(2π)−1 ∝02π¦p(θ)¦2 dθ¦pϵ Pn}, where Pn denotes th...
AbstractThe well-known Marcinkiewicz-Zygmund inequality ∫02x|T(x)|pdx1p⩽Ap1n∑k=02nT2kπ2n+1p1p, 1<p<+...
AbstractFor trigonometric polynomials on [-π,π]≡T, the classical Jackson inequality En(f)p⩽Cωr(f,1/n...
AbstractLet Tn be the set of all trigonometric polynomials of degree at most n. Denote by Φ+ the cla...
AbstractThe inequality Tn(xy) ⩽ Tn(x) Tn(y), x, y ⩾ 1, where Tn(x) is the Tchebycheff polynomial of ...
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