Our aim in this paper is to deal with Sobolev embeddings for Riesz potentials of variable order with functions in variable exponent Musielak-Orlicz-Morrey spaces.
Our aim in this paper is to deal with Sobolev embeddings for Riesz potentials of variable order with functions in variable exponent Musielak-Orlicz-Morrey spaces.
We study the linearized maximal operator associated with dilates of the hyperbolic cross multiplier in dimension two. Assuming a Lipschitz condition and a lower bound on the linearizing function, we obtain Lp(R2)Lp(R2...
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We study the linearized maximal operator associated with dilates of the hyperbolic cross multiplier in dimension two. Assuming a Lipschitz condition and a lower bound on the linearizing function, we obtain Lp(R2)Lp(R2) bounds for all 1
For a normalized root system R in R-N and a multiplicity function k >= 0 let N = N + Sigma(alpha is an element of R)k(alpha). Denote by dw(x) = Pi(alpha is an element of R) vertical bar vertical bar(k(alpha)) dx th...
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For a normalized root system R in R-N and a multiplicity function k >= 0 let N = N + Sigma(alpha is an element of R)k(alpha). Denote by dw(x) = Pi(alpha is an element of R) vertical bar < x, alpha >vertical bar(k(alpha)) dx the associated measure in RN. Let stand for the Dunkl transform. Given a bounded function m on R-N, we prove that if there is s > N such that m satisfies the classical Hormander condition with the smoothness s, then the multiplier operator T(m)f = F-1(mFf) is of weak type (1, 1), strong type (p,p) for 1 < p < infinity, and is bounded on a relevant Hardy space H-1. To this end we study the Dunkl translations and the Dunkl convolution operators and prove that if F is sufficiently regular, for example its certain Schwartz class seminorm is finite, then the Dunkl convolution operator with the function F is bounded on L-p(dw) for 1 <= p <= infinity. We also consider boundedness of maximal operators associated with the Dunkl convolutions with Schwartz class functions. (C) 2019 Elsevier Inc. All rights reserved.
We investigate the convergence rate of the generalized Bochner-Riesz means S-R(delta,gamma) on L-P-Sobolev spaces in the sharp range of delta and p (p >= 2). We give the relation between the smoothness imposed on f...
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We investigate the convergence rate of the generalized Bochner-Riesz means S-R(delta,gamma) on L-P-Sobolev spaces in the sharp range of delta and p (p >= 2). We give the relation between the smoothness imposed on functions and the rate of almost-everywhere convergence of S-R(delta,gamma). As an application, the corresponding results can be extended to the n-torus T-n by using some transference theorems. Also, we consider the following two generalized Bochner-Riesz multipliers, (1 - vertical bar xi vertical bar(gamma 1))(+)(delta) and (1 - vertical bar xi vertical bar(gamma 2))(-)(delta), where gamma(1), gamma(2), delta are positive real numbers. We prove that, as the maximal operators of the multiplier operators with respect to the two functions, their L-2(vertical bar x vertical bar(-beta))-boundedness is equivalent for any gamma(1), gamma(2) and fixed delta.
We study the problem of dominating the dyadic strong maximal function by (1, 1)-type sparse forms based on rectangles with sides parallel to the axes, and show that such domination is impossible. Our proof relies on a...
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We study the problem of dominating the dyadic strong maximal function by (1, 1)-type sparse forms based on rectangles with sides parallel to the axes, and show that such domination is impossible. Our proof relies on an explicit construction of a pair of maximally separated point sets with respect to an appropriately defined notion of distance. (C) 2019 Elsevier Inc. All rights reserved.
We study mapping properties of commutators in certain vanishing subspaces of Morrey spaces, which were recently used to solve the delicate problem of describing the closure of nice functions in Morrey norm. We show th...
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We study mapping properties of commutators in certain vanishing subspaces of Morrey spaces, which were recently used to solve the delicate problem of describing the closure of nice functions in Morrey norm. We show that the vanishing properties defining those subspaces are preserved under the action of maximal commutators and commutators of fractional integral operators. (C) 2019 Elsevier Ltd. All rights reserved.
The purpose of this paper is to obtain an integral representation for the difference f(L-1) - f(L-2) of functions of maximal dissipative operators. This representation in terms of double operator integrals will allow ...
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The purpose of this paper is to obtain an integral representation for the difference f(L-1) - f(L-2) of functions of maximal dissipative operators. This representation in terms of double operator integrals will allow us to establish Lipschitz-type estimates for functions of maximal dissipative operators. We also consider a similar problem for quasicommutators, i.e., operators of the form f(L-1)R - Rf(L-2).
We present sharp quantitative weighted norm inequalities for the Hardy-Littlewood maximal function in the context of locally compact abelian groups, obtaining an improved version of the so-called Buckley's theorem...
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We present sharp quantitative weighted norm inequalities for the Hardy-Littlewood maximal function in the context of locally compact abelian groups, obtaining an improved version of the so-called Buckley's theorem. On the way, we prove a precise reverse Holder inequality for Muckenhoupt A(infinity) weights and provide a valid version of the "open property" for Muckenhoupt A(p) weights.
Abstract: The explicit upper Bellman function is found for the natural dyadic maximal operator acting from $\mathrm {BMO}(\mathbb {R}^n)$ into $\mathrm {BLO}(\mathbb {R}^n)$. As a consequence, it is shown that...
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Abstract: The explicit upper Bellman function is found for the natural dyadic maximal operator acting from $\mathrm {BMO}(\mathbb {R}^n)$ into $\mathrm {BLO}(\mathbb {R}^n)$. As a consequence, it is shown that the $\mathrm {BMO}\to \mathrm {BLO}$ norm of the natural operator equals $1$ for all $n$, and so does the norm of the classical dyadic maximal operator. The main result is a partial consequence of a theorem for the so-called $\alpha$-trees, which generalize dyadic lattices. The Bellman function in this setting exhibits an interesting quasiperiodic structure depending on $\alpha$, but also allows a majorant independent of $\alpha$, hence a dimension-free norm constant. Also, the decay of the norm is described with respect to the growth of the difference between the average of a function on a cube and the infimum of its maximal function on that cube. An explicit norm-optimizing sequence is constructed.
The Hardy-Littlewood maximal function, defined as the supremum of integral averages of a function over balls, is a classical and well-known tool in analysis. One essential property of the maximal function is the Hardy...
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The Hardy-Littlewood maximal function, defined as the supremum of integral averages of a function over balls, is a classical and well-known tool in analysis. One essential property of the maximal function is the Hardy-Littlewood maximal inequality, which states that a weak type Lebesgue space norm estimate holds for p = 1, and a strong type estimate holds for all p > 1. In this thesis, a more general spherical maximal operator is studied. Instead of balls, the integral average is taken over the boundary of the ball, with respect to the n − 1 -dimensional spherical measure. The main result of this work is a Lebesgue space norm estimate for the spherical maximal function. We study the Fourier transform of a radially restricted spherical average operator. The dyadic Littlewood-Paley decomposition and a decay estimate for the Fourier transform of the spherical measure are used to prove L p → L q estimates on certain pairs (p, q). These results are then generalized to the full maximal operator, and interpolated for more general pairs (p, q).
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