Hölder regularity of quasiminimizers under generalized growth conditions

P Harjulehto, P Hästö, O Toivanen - Calculus of Variations and Partial …, 2017‏ - Springer
We prove Harnack's inequality for local (quasi) minimizers in generalized Orlicz spaces
without polynomial growth or coercivity conditions. As a consequence, we obtain the local …

Generalized Orlicz spaces and related PDE

P Harjulehto, P Hästö, R Klén - Nonlinear Analysis: Theory, Methods & …, 2016‏ - Elsevier
We prove the boundedness of the maximal operator in generalized Orlicz spaces defined on
subsets of R n. The proof is based on an extension result for Φ-functions. We study …

Extrapolation and interpolation in generalized Orlicz spaces

D Cruz-Uribe, P Hästö - Transactions of the American Mathematical Society, 2018‏ - ams.org
We prove versions of the Rubio de Francia extrapolation theorem in generalized Orlicz
spaces. As a consequence, we obtain boundedness results for several classical operators …

New martingale inequalities and applications to Fourier analysis

G **e, F Weisz, D Yang, Y Jiao - Nonlinear Analysis, 2019‏ - Elsevier
Abstract Let (Ω, F, P) be a probability space and φ: Ω×[0,∞)→[0,∞) be a Musielak–Orlicz
function. In this article, the authors prove that the Doob maximal operator is bounded on the …

Double phase image restoration

P Harjulehto, P Hästö - Journal of Mathematical Analysis and Applications, 2021‏ - Elsevier
In this paper we explore the potential of the double phase functional in an image processing
context. To this end, we study minimizers of the double phase energy for functions with …

Atomic characterizations of weak martingale Musielak–Orlicz Hardy spaces and their applications

G **e, D Yang - 2019‏ - projecteuclid.org
Abstract Let (Ω, F, P) be a probability space, and let φ: Ω×[0,∞)→[0,∞) be a Musielak–Orlicz
function. In this article, we establish the atomic characterizations of weak martingale …

[HTML][HTML] A blow-up result for nonlinear generalized heat equation

MK Alaoui, SA Messaoudi, HB Khenous - Computers & Mathematics with …, 2014‏ - Elsevier
A blow-up result for nonlinear generalized heat equation - ScienceDirect Skip to main contentSkip
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The Riesz potential in generalized Orlicz spaces

P Harjulehto, P Hästö - Forum Mathematicum, 2017‏ - degruyter.com
In this article we prove a Riesz potential estimate and a Sobolev inequality for general
generalized Orlicz spaces. Our assumptions are natural generalizations of the log-Hölder …

Doob's maximal inequality and Burkholder–Davis–Gundy's inequality on Musielak–Orlicz spaces

L He, L Long, G **e, D Yang - Mathematische Zeitschrift, 2023‏ - Springer
Given a probability space (Ω, F, P) and an unbounded Musielak–Orlicz function φ:
Ω×[0,∞)→[0,∞], the authors establish Doob's maximal inequality and weak type Doob's …

Lower and upper bounds for the blow-up time to a viscoelastic Petrovsky wave equation with variable sources and memory term

A Rahmoune - Applicable Analysis, 2023‏ - Taylor & Francis
Under Dirichlet boundary conditions, we consider here a new type of viscoelastic Petrovsky
wave equation involving variable sources and memory term utt+ Δ 2 u−∫ 0 tg (t− s) Δ 2 u (x …