41 citations · 123 across the 24 of their papers we have counts for
27 papers
A note on new mapping properties for Wolff potential
Petteri Harjulehto, Ritva Hurri-Syrjänen
We study integrability properties of the Wolff potential in context of Choquet integrals with respect to the Hausdorff content. As an application we give integrability results to t…
A note on Sobolev inequalities in the lower limit case
Petteri Harjulehto, Ritva Hurri-Syrjänen
We study Poincare-Sobolev type inequalities for compactly supported smooth functions which are defined in the Euclidean -space and whose absolute value of gradient are Choquet $…
Relaxation of quasi-convex functionals with variable exponent growth
Giacomo Bertazzoni, Petteri Harjulehto, Peter Hästö +1
We prove a relaxation result for a quasi-convex bulk integral functional with variable exponent growth in a suitable space of bounded variation type. A key tool is a decomposition…
On Lebesgue points and measurability with Choquet integrals
Petteri Harjulehto, Ritva Hurri-Syrjänen
We consider Choquet integrals with respect to dyadic Hausdorff content of non-negative functions which are not necessarily Lebesgue measurable. We study the theory of Lebesgue poin…
On Hausdorff content maximal operator and Riesz potential for non-measurable functions
Petteri Harjulehto, Ritva Hurri-Syrjänen
We introduce Riesz potentials for non-Lebesgue measurable functions by taking the integrals in the sense of Choquet with respect to Hausdorff content and prove boundedness results…
On Choquet integrals and pointwise estimates
Petteri Harjulehto, Ritva Hurri-Syrjänen
We consider inequalities where integrals are defined in the sense of Choquet with respect to Hausdorff content. We study cases where continuously differentiable functions are defin…
On Choquet integrals and Sobolev type inequalities
Petteri Harjulehto, Ritva Hurri-Syrjänen
We consider integrals in the sense of Choquet with respect to the -dimensional Hausdorff content for continuously differentiable functions defined on open, connected sets in the…
Monotone approximation of differentiable convex functions with applications to general minimization problems
Petteri Harjulehto, Peter Hästö, Andrea Torricelli
We study minimizers of non-autonomous energies with minimal growth and coercivity assumptions on the energy. We show that the minimizer is nevertheless the solution of the relevant…
A revised condition for harmonic analysis in generalized Orlicz spaces on unbounded domains
Petteri Harjulehto, Peter Hästö, Artur Słabuszewski
Conditions for harmonic analysis in generalized Orlicz spaces have been studied over the past decade. One approach involves the generalized inverse of so-called weak -functions.…
Convergence of generalized Orlicz norms with lower growth rate tending to infinity
Giacomo Bertazzoni, Petteri Harjulehto, Peter Hästö
We study convergence of generalized Orlicz energies when the lower growth-rate tends to infinity. We generalize results by Bocea--Mihăilescu (Orlicz case) and Eleuteri--Prinari (va…
Bounded variation spaces with generalized Orlicz growth related to image denoising
Michela Eleuteri, Petteri Harjulehto, Peter Hästö
Motivated by the image denoising problem and the undesirable stair-casing effect of the total variation method, we introduce bounded variation spaces with generalized Orlicz growth…
Bloch estimates in non-doubling generalized Orlicz spaces
Petteri Harjulehto, Peter Hästö, Jonne Juusti
We study minimizers of non-autonomous functionals \begin{align*} \inf_u \int_Ωφ(x,|\nabla u|) \, dx \end{align*} when has generalized Orlicz growth. We consider the case where…
Stability of solutions to obstacle problems with generalized Orlicz growth
Petteri Harjulehto, Arttu Karppinen
We consider nonlinear equations having generalized Orlicz growth (also known as Musielak--Orlicz growth). We prove that if differential operators converge locally u…
On Choquet integrals and Poincaré-Sobolev inequalities
P. Harjulehto, R. Hurri-Syrjänen
We consider integral inequalities in the sense of Choquet with respect to the Hausdorff content . In particular, if is a bounded John domain in $\mathbb{R…
Minimizers of abstract generalized Orlicz--bounded variation energy
Michela Eleuteri, Petteri Harjulehto, Peter Hästö
A way to measure the lower growth rate of is to require to be increasing in . If this condition holds wit…
Estimates for the variable order Riesz potential with applications
Petteri Harjulehto, Ritva Hurri-Syrjänen
We study weak-type estimates and exponential integrability for the variable order Riesz potential. As an application we prove an exponential integrability result with respect to th…
Sharp growth conditions for boundedness of maximal function in generalized Orlicz spaces
Petteri Harjulehto, Arttu Karppinen
We study sharp growth conditions for the boundedness of the Hardy-Littlewood maximal function in the generalized Orlicz spaces. We assume that the generalized Orlicz function $ϕ(x,…
A new class of double phase variable exponent problems: Existence and uniqueness
Ángel Crespo-Blanco, Leszek Gasiński, Petteri Harjulehto +1
In this paper we introduce a new class of quasilinear elliptic equations driven by the so-called double phase operator with variable exponents. We prove certain properties of the c…
The weak Harnack inequality for unbounded supersolutions of equations with generalized Orlicz growth
Allami Benyaiche, Petteri Harjulehto, Peter Hästö +1
We study unbounded weak supersolutions of elliptic partial differential equations with generalized Orlicz (Musielak--Orlicz) growth. We show that they satisfy the weak Harnack ineq…
The Kellogg property under generalized growth conditions
Petteri Harjulehto, Jonne Juusti
We study minimizers of the Dirichlet phi-energy integral with generalized Orlicz growth. We prove the Kellogg property, the set of irregular points has zero capacity, and give char…
Extension in generalized Orlicz spaces
Petteri Harjulehto, Peter Hästö
We prove that a -function can be extended from a domain to all of while preserving crucial properties for harmonic analysis on the generalized Orlicz space $L^…
Double phase image restoration
Petteri Harjulehto, Peter Hästö
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…
Hölder continuity of -minimizers of functionals with generalized Orlicz growth
Petteri Harjulehto, Peter Hästö, Mikyoung Lee
We show local Hölder continuity of quasiminimizers of functionals with non-standard (Musielak--Orlicz) growth. Compared with previous results, we cover more general minimizing func…
Embeddings into Orlicz spaces via the modified Riesz potential
Petteri Harjulehto, Ritva Hurri-Syrjänen
We study point-wise estimates for the modified Riesz potential. We show that the point-wise estimates imply embeddings into Orlicz spaces from the L^1_p-space where the functions a…