The goal of this paper is to obtain atomic and wavelet characterizations Musielak–Orlicz Hardy spaces. Recently, in 2018, Fu Yang obtained spaces for growth functions uniformly upper type $$p_-$$ lower $$p_+$$ with $$0<p_- \le p_+\le 1$$ . What different from the existing works that we merely assume p_+<\infty $$ One important tools make it possible refine convexity Orlicz by obtaining canonica...

It can be checked that this is a valid norm (on the set of random variables for which the left side of the above display is finite). Of special interest to us will be the Orlicz norms corresponding to the functions {ψp : p ≥ 1} where ψp(x) = exp(xp) − 1. Lemma 8.1 of Kosorok (2008) provides a necessary and sufficient condition for the ψp Orlicz norm to be finite in terms of the tail-behavior of...

Our concern in this paper lies with imbeddings of general spaces of Besov and Lizorkin-Triebel type with dominating mixed derivatives in the first critical case. We employ multivariate exponential Orlicz and Lorentz-Orlicz spaces in the role of targets. We study basic properties of the target spaces, in particular, we compare them with usual exponential spaces, showing that in this case the mul...

We prove variants of Korn’s inequality involving the deviatoric part of the symmetric gradient of fields u : R2 ⊃ Ω → R2 belonging to Orlicz-Sobolev classes. These inequalities are derived with the help of gradient estimates for the Poisson equation in Orlicz spaces. We apply these Korn type inequalities to variational integrals of the form ∫ Ω h ( |εD(u)| ) dx occurring in General Relativity a...

An old problem of P. Levy is to characterize those Banach spaces which embed isometrically in Lp. We show a new criterion in terms of the second derivative of the norm. As a consequence we show that, if M is a twice differentiable Orlicz function with M (0) = M (0) = 0, then the n-dimensional Orlicz space l M , n ≥ 3 does not embed isometrically in Lp with 0 < p ≤ 2. These results generalize an...

Using the idea of the optimal decomposition developed in recent papers [EK2] by the same authors and in [CUK] we study the boundedness of the operator Tg(x) = ∫ 1 x g(u) du/u, x ∈ (0, 1), and its logarithmic variant between Lorentz spaces and exponential Orlicz and Lorentz-Orlicz spaces. These operators are naturally linked with Moser’s lemma, O’Neil’s convolution inequality, and estimates for ...

We investigate how planar Sobolev-Orlicz homeomorphisms map sets of Hausdorff dimension less than two. With the correct gauge functions the generalized Hausdorff measures of the image sets are shown to be zero.

In this article we investigate the Fourier series and transforms for the functions defined on the [0, 2π] d or R d and belonging to the exponential Orlicz and some other rearrangement invariant (r.i.) spaces.

Abstract. In this paper, we give necessary and sufficient conditions for a point in a Musielak-Orlicz sequence space equipped with the Orlicz norm to be an H-point. We give necessary and sufficient conditions for a Musielak-Orlicz sequence space equipped with the Orlicz norm to have the Kadec-Klee property, the uniform Kadec-Klee property and to be nearly uniformly convex. We show that a Musiel...