Using [Authorize] without passing any parameters boils down to a call that checks whether or not the user is authenticated. From inside a service, that would look something like this:
// If any of the properties being accessed are null, assume that the user
// is not authenticated.
var isAuthenticated = httpContext?.User?.Identity?.IsAuthenticated ?? false;
To access HttpContext inside of a service, you can use IHttpContextAccessor. Here's a complete example:
public class Service
{
    private readonly IHttpContextAccessor httpContextAccessor;
    public Service(IHttpContextAccessor httpContextAccessor)
    {
        this.httpContextAccessor = httpContextAccessor;
    }
    public void ServiceFunction()
    {
        var httpContext = httpContextAccessor.HttpContext;
        var isAuthenticated = httpContext?.User?.Identity?.IsAuthenticated ?? false;
        if (isAuthenticated)
        {
            // The user is authenticated.
        }
    }
}
If you want to apply an authorisation policy, you can use IAuthorizationService. Here's a complete example of that:
public class Service
{
    private readonly IHttpContextAccessor httpContextAccessor;
    private readonly IAuthorizationService authzService;
    public Service(IHttpContextAccessor httpContextAccessor,
        IAuthorizationService authzService)
    {
        this.httpContextAccessor = httpContextAccessor;
        this.authzService = authzService;
    }
    public async Task ServiceFunction()
    {
        var httpContext = httpContextAccessor.HttpContext;
        var isAuthenticated = httpContext?.User?.Identity?.IsAuthenticated ?? false;
        if (isAuthenticated)
        {
            // The user is authenticated.
            var authzResult = await authzService.AuthorizeAsync(
                httpContext.User,
                "PolicyName");
            if (authzResult.Succeeded)
            {
                // The user is authorised.
            }
        }
    }
}
Note: To use IHttpContextAccessor, you might need to add services.AddHttpContextAccessor(); to your Startup.ConfigureServices method.